Despite leaving before Harry

I think that's wrong. Here's chapter 89:

He'd felt the boy give himself over fully to the killing intention. That was when the Defense Professor had begun burning through the substance of Hogwarts, trying to reach the battle in time.

In chapter 90 Quirrell claims to have left as soon as he discovered "that Miss Granger was on the verge of death", whatever that means, but it seems clear he's lying.