If I wanted to write a HP fan fic, i'd go in an alternate universe, where Neville is the hero of the story and make Harry a great supporting character. I would change the dynamics of all the characters, reverse and warp the concept of good and evil with Dumbledore being a seemingly benign dictator seeking to dominate the magical world with his Army of disciples and Voldemort, his ex pupil and ex-lover (yes, I'd go there ) building a force against him from the outsiders of magical society. Theme wise, I'd stress more on the areas untouched by Rowling: the notion of social alienation, how power can easily be abused, and the complexities between true heroism and villains.
Luckily for everyone, I don't write fan fics
I actually think that would make an excellent fanfiction!