Or you could skip past all of that, just as the wizards do, and deal with wizarding issues.
Dark Wizards, Muggles actually being kidnaped for experiments, Politics, Trade, Magical creatures, Non-parallel magical engineering,
Eldritch Horror [Campy, maybe, but you know it would be nuts to see some school for "gifted children" settled in maine, and strange things happen. Things that no mage could make happen]
Every setting can be broken. Meta-plot logic can be applied to any literary, plot driven source.
Forget harry potter and the natural 20. Forget the years of analysis.
Hogwarts can be tied up in all of it's shenanigans, but the fantastic thing is that hogwarts is one school. As a GM you can make it as big or small as you want. Maybe Voldemort in all his power is a regional threat. Hogwarts IS pretty fucking english.
maybe, every other country has their own deterrents for such threats.
Don't call it harry potter the game, or hogwarts the game.
Go more expansive.
>World of Wizardry and Witchcraft.
I would definitely agree with the storyteller system being a primary influence on rules. I would focus more on the lives of the wizards outside of school, but would have a book for games in the school.
I would make the houses almost important as say, one's birth month in astrology. There are many houses outside of the hogwarts 4, but wizards do have a tendency to have extreme personalities based on cultural archetypes.
Focus would be on the wizards fresh out of the schools, and the various careers that wizards fall into.
I would also have "Sorcerer space" Wizards don't live in between enchanted or glamoured space. They live in parallel subspaces. The "wizarding world" is the same size as earth itself. The reason they interact with the muggle world is because it is superimposed on top of it, and ever now and then cracks slip up.
Having a fantasy world just as big and old as real earth, in culture gives big opportunities for exploration.