I rarely read AR, to be honest. A nagging part of me feels that many authors use it to write their own story, with their own plot, without having to deal with the tedious task of fleshing out their own believable characters. The original story is used as a crutch; the new fiction shamelessly calls upon the reader's knowledge to supplement its own lacking characterization. It's not the exercise in transplanting characters into unfamiliar situations and exploring their innate characteristics that AR is intended to be.
But, what was wonderful about your fic is that I felt like you really did intend to explore the characters first, the AR plot second. It was evident the amount of effort you put into the fic. Historical fiction requires a delicate balance between providing enough historical reference for the setting to be believed (yet not overburdening the reader), while maintaining the characters in a manner that transcends time/situation. You succeeded at both, imo.
I'm not sure that this is quite as successful at being a snarry (Mentor!Snape) as it is at being a period piece. The situation is a bit too far removed from that of the books, I think. There is little that compares to the Harry Potter-verse (with the exception, in many respects, of something like WWII Germany), so trying to pick apart what is innate and what is a result of circumstance is...difficult. I appreciated the nods to the series (Harry's skill with a broom), but...Personalities are formed through life experiences - these men didn't share enough with the men of JKR's novels for me to be convinced, despite some common elements between the counterparts.
Still, it was a wonderful story, in its own right. Well researched, polished, well thought out - if anything, I would argue it begged to be longer. Your characters felt, to me, like they were their own unique men, which may be disappointing in the context of the games, but in general is an amazing thing. I'd love to read more from you.