very good story.

Very well done. I love the concept of unity amid diverse strengths. Do write us a new tale :-)

Oh, yes. The last Headmaster talked about unity; this one means it. Excellent.

A nice, gentle ending. The moment when Severus thinks that, in truth, even if Hermione hadn't made friends her fate wouldn't have been anything like as bad as his, but he doesn't say it because he doesn't want to disrupt the moment, is especially clever.

The introducing of a new system of awarding points and prizes at Hogwarts is a great idea because it consents to maintain the fascination of the sorting and a healthy competition without feeding enmity.
It has been a good first move destined to mark a positive sign in his ruling of the school.
Who but Snape could understand the danger to keep on consenting division against union of the houses? It needed a headmaster that had suffered a lot and was a victim of this way of thinking to begin the new course.
The whole domestic scene is very peaceful and consoling. Time didn’t change them much and they keep their respective grumpiness and bravery and I think that the final words said in a sweet moment are a gem. Wise choice stopping the tale just little before of knowing in which house their son will be sorted: it strengthens your nice story.

Unity would be a good end to the series. I foresee a problem with the new method of awarding the House Cups in the future though; they must eventually reach an upper limit, beyond which no points are possible to award, unless the teachers take a deliberate decision to increase the amount given per act. But that only devalues the point system in the long run, in the same way that printing extra cash notes devalues a currency.