A problem with Quirrell's heroic alter ego being Tom Riddle, even if the only ones who know Tom Riddle is Voldemort are the inner circle of the Order of the Phoenix, is, why wouldn't madam Bones tell Dumbledore that Tom Riddle is currently inhabiting Quirrell's body?

Riddle appears to have convinced Bones that he's a genuinely good guy who's dying, and wants to live out the final months of his life without his true identity being known. She will likely respect his wishes because, hey, he was a real hero once.

Or Bones will tell Dumbledore and this will lead to a climax suitable for the end of a Hogwarts school year.

But unfortunately, it seems that in this fic even smart people are capable of shooting themselves in the foot not sharing information freely enough. I mean, if Dumbledore and Harry sat down and shared all the information they have, they'd have identified Quirrell as Riddle/Voldemort by now.