A very clever, interesting story with deft characterizations; you do a good job with the implications of time travel. I'm particularly fond of the scene with Minerva and of your idea that the teachers deal with the workload by using time-turners. It makes perfect sense: in canon, the school is absurdly understaffed, and unless we're willing to believe that the Heads of Houses work 80-hour weeks, there's no other way they could manage everything.
Here's one of my favorite lines: The determined good cheer dropped away, and for a few moments Hermione saw a very weary woman, who was conscious of her own mistakes and losses, before McGonagall said quietly, "They would forgive you, I think, as I shall pray they will forgive me, with far less reason. We all make mistakes, Miss Granger." This is the sort of very real moment that gives effective texture to a story.
I like that your Hermione isn't perfect, that Ron is given some depth, and that Severus is. . .Severus.