Harry can save Hermione by offering false testimony against Quirrell. There's a taboo social tradeoff. The odd thing is that he has to do it by telling lies about Quirrell that we know are mostly true.
Harry can give false testimony under Veritaserum, because he's an Occlumens, which of those present only Dumbledore and McGonagall and the Malfoys know (and the Malfoys wouldn't be believed).
So, what can he falsely testify that would save Hermione?
If Harry falsely testifies against Quirrell, neither Dumbledore nor McGonagall would suspect it of being a lie, especially if Harry explained he had kept silent in hopes of making Quirrell think he was actually won over to Voldemort's side. It also fits the convenient fact that it was Quirrell who discovered the bodies. And because Quirrell really did rescue Bellatrix Black, Harry can offer plenty of true testimony about the Azkaban mission as stuff that Quirrell told him to impress him. So his testimony will seem verifiable as well as Veritaserum-proved. Harry knows Quirrell wouldn't come in to defend himself from the charge Harry thinks he's innocent of (Hermione and Draco), because he'd be sent to Azkaban for the charge Harry knows he's guilty of (rescuing Bellatrix Black).
And while Harry doesn't want to turn on Quirrell... he knows Quirrell can defend himself a lot better than Hermione can. He could use his Patronus to deliver a message to Quirrell to run and hide right after he testifies (or, with a Time-Turner, right before).
For added flavor, Harry could truthfully testify about rescuing Bellatrix Black - and claim that he was Imperius'd into his role, just like good old Lucius!
I don't think "Harry sacrifices Quirrell" is the actual answer, because Harry making a big deal in his mind of "sacrificing" Quirrell would feel a little cheap for those of us who know he should turn on Quirrellmort. Dramatically it would work better for Harry to sacrifice someone we think is genuinely valuable to him, or to pull out some interesting social leverage over the Wizengamot voters. But false testimony against Quirrell is for Harry a lot more "taboo" than calling in Imperius-debts, and doesn't require a side-deal the way that pressuring Dumbledore with false testimony over Narcissa would, or the kind of shenanigans of invoking a duel with Draco over the insult to the Ancient House of Potter.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: