Harry made some serious mistakes in chapter 105.

First, the parseltongue honesty-binding could just be Quirrell's (selective!) wandless magic--I mean, he just forged a note "from yourself" (and why do you even MAKE a self-recognition ("I am a potato") policy if you just forget all about it once you're in a life-stakes intrigue) so you need a lot of extra suspicions going forward. But assuming it's real... there are crucial questions Harry can now profitably ask, with his help conditional on getting immediate Parseltongue answers, along the lines of:

"Why did you set up this elaborate ruse instead of just asking me? Most of what you're saying right now sounds like something I would've probably agreed to if you were open about it, but no, you had to pretend you were dying and kill my friend, so it sure seems like you're planning nefarious things I'd rather not aid even at the cost of my life and the hostages' lives... does my CURRENT utility function actually prefer your planned results to the death of me and the hostages?"

(This isn't the perfect phrasing; for one thing Quirrell doesn't necessarily know Harry's utility function to high accuracy, for another Harry might have disagreed to the "open" proposal at weaker dispreference than "this is worse than my death". But something similar...)

Iff Quirrell is at all "innocent" at this point, he'd want to answer these, and never mind the "my policy is never to reveal that much or people will know I'm guilty later when I actually need to keep mum" stuff; these stakes seem high enough to outweigh any future similar dealings. If he's guilty, then just die like you'd apparently prefer.

[the only edits I made here after getting responses were to correct my spelling of "Quirrell", and this note]