By Mr Khan
This is me throwing my hat in the time-skip speculation ring, but trying to tackle it from a different angle by trying to fill in some of the mysteries about the skip, rather than writing a reunion story.
The day of the Sabaody Archipelago Incident was the crowning achievement of Bartholomew Kuma's career as a Shichibukai. In scattering the Straw Hats to the four winds, he had fulfilled his purpose as a Shichibukai, just before his death.
Bartholomew Kuma, Kuma the Tyrant, Kuma the Heartless. In his days as a pirate, he had ruled the Grand Line with an iron fist. His devil fruit made it possible: he simply needed to touch a foe, and they would be his foe no more. No attack could harm him, once he had honed his blocking reflexes, and he refined his power to allow himself to be wherever he needed to be. Nothing could escape his vigilance.
It was only natural that the World Government sought his talents. If they had Kuma on their side, they would be able to enforce their rule anywhere in the world with absolute impunity. Kuma had near-instantaneous crisis-response capabilities, and could be the ultimate Enforcer. Kuma's strength meant that he scorned the World Government, however. He had no need to serve them when they could provide him with nothing he couldn't seize for himself if he wished. He rejected their offer of the rank of Shichibukai many times, and the Admiralty almost gave up hope.
But there was another side: Kuma the Tyrant was also Kuma the Softy, Kuma the Kind-hearted. No-one ever knew what happened to his victims when they were at the receiving end of his paw power, there was only the presumption that they had been banished beyond the ends of the earth. No-one ever came back. But it was not Kuma's way to destroy his foes utterly. Kuma felt that lethal tactics were a sign of the uncivilized: with his powers he did not need to kill his foes, except for those too powerful to be affected by his base ability. When possible, he liked to send them away, where they would never trouble him again, but could at least continue to live their lives.
"If you were going on vacation, where would you like to go?" Most people assumed this was a rhetorical or ironic question, meant to instill further menace in his foes before he banished them to their doom, but it was actually quite true. Given his ability to practically warp around at will, he had a vast geographical knowledge. In all the world, he knew of one island that was utterly inaccessible to most of the world, similar to Amazon Lily: a tropical paradise lost in the calm belt. Here a great many of his former foes dwelt in a sort of prison colony, trapped, but happy. He even shipped them supplies periodically, though he never came to see them himself.
It was that soft-heartedness that had gotten Kuma in the position he was in. He had been able to refuse the offers of the World Government for a long time, but one day there had been an incident. On that day, now almost 13 years ago, Kuma had come close to losing that which was most precious to him in the entire world. That day could have been horribly tragic, but someone prevented it: Monkey D. Dragon.
He owed Dragon a debt that he could never repay, though he came close on that day in Sabaody Archipelago. More than anything, Dragon wanted a mole: someone so deeply embedded in the ranks of the World Government as to be beyond suspicion. Someone who would be able to betray them just when the moment was right, and have all evidence of his treachery destroyed soon after Dragon knew of the top-secret experiments of Dr. Vegapunk, the process of making cyborgs. Dragon knew that Vegapunk was looking for a test subject, and also knew that the World Government sought Kuma as a Shichibukai. Putting the pieces together, he asked Kuma to give his life to help Dragon's cause.
Kuma was eager to comply.
Kuma turned up at Marineford unexpectedly, volunteering to join the World Government as a Shichibukai. Furthermore, he volunteered for Vegapunk's offer. The World Government was surprised and suspicious, but Kuma proved so unflinchingly loyal in the first few missions they set to him that they eventually found him to be the invaluable Shichibukai that they had always dreamt of, and they knew that once Vegapunk finished his conversion of Kuma, that they would never have to fear his treachery again.
It meant he was the ultimate mole. Once he was converted, he would be beyond suspicion. If he timed it properly, it meant he would have one chance, one opportunity to betray the World Government, and immediately afterward could request to have the procedure finalized. In his arrogance, Vegapunk would destroy any evidence of Kuma's betrayal.
Despite his loyalty, he still disappointed on occasions, rare though that was. The latest disappointment had been Thriller Bark, where he had showed the Straw Hats' mercy in an effort to cruelly toy with the rookies, or at least that was how his bosses interpreted his mercy. Vegapunk had said that this instance of disobedience meant that it was time to complete the process, but the Admiralty, so impressed with his loyalty, put it off, giving him one more chance.
"If you encounter the Straw-hat pirates again, dispose of them."
"Dispose." Now there was a broad term. To Kuma, it meant simply to banish them. But he was reluctant to do so. Luffy was the child of Dragon, his savior, in Luffy there was a great potential that remained mostly untapped, one that would fit in beautifully with Dragon's larger agenda.
He pondered the implications of that order many times. Would he really have to send the straw-hats away forever the next time he encountered them? It would be a tragedy. In his own way, Luffy was spreading the revolution, same as his father. The Fall of Enies Lobby was something more grandiose than the Revolutionaries preferred, but it had been a tremendous boost to the cause.
Kuma was still lost in thought when the emergency call went out: Tenryuubito Crisis Response. News came in on the den-den mushi that that Monkey D. Luffy had assaulted a Tenryuubito. Kuma grew afraid: the straw hats would not survive a full assault from an Admiral: all the pluck and grit in the world was not enough to save them from Akainu, Kizaru, or Aokiji.
For a time, he was paralyzed: resigned to the fact that the plucky rookies would fall, either to die on the spot or be dragged to Impel Down as an exhibition. They couldn't possibly survive: even with strength enough to topple CP9 and Gecko Moria, they would need years of training to play with the big boys: the top four Shichibukai, the Admiralty, the Yonkou. Years indeed, and they would be lucky to have minutes. Kizaru was sent out, as well as Sentoumaru leading a squad of Pacifistas.
Years of training.
Now was the time.
What if he happened to be there, choosing to be at Sabaody Archipelago at that instant? The World Government had not ordered that he stay, and they had ordered that he dispose of the Straw Hats. He was just following orders, and through it, he could save them, and still further, could provide them with the training they needed.
SUBJECT: MONKEY D. LUFFY
ATTRIBUTES: GUM-GUM FRUIT, HAKI
He had pegged Luffy as a haki user from their last encounter. The aura the young man emitted confirmed it. But clearly Luffy was unaware of it. Haki was the prerequisite to really fight at the highest level, as the top tier of global power players all used it in some fashion, and Luffy would need the full extent of that power if he wanted to proceed, or even survive.
He needed to go somewhere where he could be hidden from the world and cultivate this Haki, and there was really only one place he could do both, as most Haki users were high profile, and a great many of them were foes of the straw-hat to begin with. Amazon Lily was the only possibility, though it was scarcely less of a death sentence than to send the boy to study under Akainu. But Kuma had a good feel of Luffy: he had the kind of stupid luck that might just allow him to be the only male to ever survive on Amazon Lily, and learn from the haki-wielding Kuja tribe.
SUBJECT: RORONOA ZORO
ATTRIBUTES: EXCELLENT SWORDSMANSHIP
Kuma had gotten a taste of Zoro's skill firsthand. Slight damage to his outer carapace, which Vegapunk had assured him was invincible, was full evidence of that. Zoro was living up to his ambition, but he needed to hone is craft to the level of excellence that Kuma had grown accustomed to on the few occasions that he had worked with Dracule Mihawk. Kuma knew it was Zoro's ambition to topple Mihawk.
Mihawk was the goal, but Mihawk could also be the means to the goal. Kuma knew his fellow Shichibukai about as well as anyone knew him, and he knew that Mihawk was the closest thing to a non-aligned actor that he had ever met. Mihawk served the World Government only because they would give him the resources to easily fight the strongest pirates in the world, specifically their transportation technologies, but while Mihawk was loyal to the World Government, he bore no real love or hatred for them. Mihawk was like a force of nature: he destroyed what was in his way, and was not to be guided by any politics. If Mihawk felt Zoro to be worthy, he would indeed train him, even if he knew he was training the man who might one day kill him.
SUBJECT: NAMI (SURNAME UNKNOWN)
ATTRIBUTES: FIGHTS WITH WEATHER-ALTERING TECHNOLOGY
Although it was not her own invention, Nami wielded the Clima Tact well. Kuma was not as familiar with Nami's skills, but he knew of a sky island that led the world in weather studies. Hopefully she would return with the power of nothing less than a goddess, otherwise Kuma might be disappointed.
SUBJECT: USOPP (SURNAME UNKNOWN), ALIAS SOGEKING
He had met the great Yasopp once in his days as a pirate, during a rather heated encounter with the Red Hair Shanks and his crew, and had seen his skill demonstrated firsthand. His son had supposedly demonstrated equally legendary sniping skills at Enies Lobby, though Kuma had not been present to witness it. Kuma knew from their encounter at Thriller Bark that Usopp was soft, despite his raw skill. The young man needed survival training, and there was no place better for that than the savage Boin Archipelago.
One of Kuma's old nakama actually dwelt there: Heracles. Heracles had refined his battle prowess right alongside Kuma in their early days together in the North Blue. For someone lacking either a devil fruit power or Haki, Heracles was probably the most able survivor Kuma had ever encountered, though they had parted ways long ago, in a vicious disagreement over the savage tactics Kuma had used in his heyday in the Grand Line. Heracles would sharpen Usopp's skill to make him Sogeking in fact as well as in name.
SUBJECT: SANJI (SURNAME UNKNOWN)
In his short time with the Revolutionaries, Kuma's best friend and greatest ally had been Emporio Ivankov. Kuma found the man to be almost unbearably strange, but at heart was one of the most worthy people he had ever met. He had even spent some time at Ivankov's home of Kamabakke Kingdom, where Emporio had impressed him with the strange and unique dishes, the Ninety Nine Attack Cuisines. Kuma had travelled most of the known world and some of the unknown world (with only the most hostile stretches of the New World outside his grasp), but had never seen food that had such a profound effect upon those who ate it. He had seen medicines with strength-augmenting capabilities, but often with horrible side-effects. The Attack Cuisines were pure, providing only good things to those who ate them. Any cook would love the chance to learn such recipes, though few would be worthy enough to claim them, but the Black Leg Sanji might just have the strength to conquer the okama chefs and learn the recipes.
SUBJECT: TONY TONY CHOPPER
Kuma knew that the young reindeer was severely undervalued by his bounty. He had seen some of his combat prowess at Thriller Bark. With a little research, he had learned that the powerful young reindeer was also a doctor. Kuma knew that Ivankov had a very advanced medical technique, but Sanji was more appropriate for Ivankov and Kamabakke Kingdom. The Tyrant could think of only one other place that might be appropriate for an aspiring young doctor to learn previously unknown skills: Torino Kingdom. Kuma had happened upon the island by chance once and found that it had all manner of exotic plants that could be found nowhere else, and the island's inhabitants, despite appearing to be quite stupid, actually knew how to make full use of these plants. Deceptively primitive, Torino Kingdom was out beyond the bleeding edge of medicinal knowledge, though few in the world aside from Kuma even knew of its existence. Chopper would emerge from that island with a body of medicinal knowledge beyond most in the world.
SUBJECT: NICO ROBIN
ATTRIBUTES: POSSESSES KNOWLEDGE THAT IS A THREAT TO THE WORLD
Even way back when he had been with the Revolutionaries, they had been seeking the infamous Devil Child of Ohara. Dragon had been aware of what was going on in Ohara before the incident, and had actually secretly been funneling funds to their research. The loss of Ohara had been a sore blow, but knowing that there was a survivor had given them hope. Dragon once said that Nico Robin would be the hope of the Revolution one day, once she fulfilled her destiny and uncovered the secrets behind the formation of the World Government. This was Robin's chance to finally join them if she chose, or they could at least supply her with information that would be of invaluable aid to the Straw Hats later on. The hope of the revolution needed to make contact.
The problem was that Kuma was no longer in contact with them. Dragon had been strict on that point, that there should be no chance that Kuma would be able to betray the Revolutionaries simply because he knew where their operations were located. As a Shichibukai, however, Kuma at least knew of where the Revolutionaries were causing trouble. Top-secret reports had been coming out of Tequila Wolf about a year leading up to the Sabaody incident, reports of the Revolutionaries raiding the construction project and liberating some of the slaves. The World Government was keeping the reports secret to save face, not only to avoid shame from the general public, but to not let the Tenryuubito know that their so-precious project was being disrupted. If Robin were sent there, surely the Revolutionaries would figure it out and secure her release.
SUBJECT: CUTTY FLAM (ALIAS FRANKY)
Kuma had been somewhat impressed with Franky's technology during their last encounter, but at the same time he realized that the shipwright's technology was woefully inadequate when compared to the sheer genius of Dr. Vegapunk. If the straw-hats seriously wanted to contend with the World Government, they would need futuristic tech of their own to counter Vegapunk's tech. Given his close relationship to Vegapunk, Kuma had learned many secrets that few others were aware of, including the mysterious genius' homeland. Vegapunk had once told him that he had left behind a lot of his old experiments in that land. A man with enough mechanical knowhow to make himself into a cyborg all on his own would certainly blossom in that futuristic land, learning retroactively from the genius himself.
SUBJECT: BROOK (SURNAME UNKNOWN)
BOUNTY: 33,000,000 (NOW DEFUNCT, PRESUMED DEAD)
ATTRIBUTES: LIVING SKELETON
He knew very little about Brook, presuming that the skeleton man was a complete unknown until he searched his own memory banks through the list of defunct bounties and uncovered a man presumed dead from 50 years before. He couldn't really send Brook to train, as he was unfamiliar with his abilities, but he could at least keep Brook hidden while the others trained. The superstitious people of Harahetternia would accept a living skeleton man as a part of the mythic world that they accepted as a reality, whereas Brook would cause a sensation if he were sent elsewhere. Kuma wasn't entirely satisfied with his decision on Brook, but he had no time to think of something better.
When he banished Monkey D. Luffy, he banished a broken man, a once-proud pirate captain who had been utterly defeated and now begged his attacker for mercy (though for the sake of his nakama, and not for himself). Kuma knew in his heart however that he would return from this calamity strong enough to endure any mental or physical hardship.
Bartholomew Kuma, as his acquaintances knew him, died after that. After Sabaody, he immediately returned to Marineford and told Vegapunk that he wanted to finish the treatment. Vegapunk was all too happy to comply, and in replacing Kuma's brain, Vegapunk destroyed any evidence that Kuma had been behind it. When the straw-hats reappeared, Kuma had nothing to say on the matter, indeed nothing to say on any matter, as he was no smarter than any of the other Pacifistas.
The return of the straw-hats was really Kuma's victory, though he was unable to appreciate it.
Author's Note: Just some harmless speculation, I hope. I don't think any of my guesses are too radical, given what we know, and given that Kuma had to know about where he was sending all of the Straw-hats, and it would fit the hints we've been given ideally. I also know that Nami's is woefully short, but there really isn't as much to say on hers, given that Kuma wouldn't know much about her himself.