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?

• That he himself tampered with Draco and Hermione's memories. But he'd better have one heck of an escape planned, even if he does have the Cloak of Invisibility and power against Dementors.
• That he did it, but he was Imperius'd into it by a mysterious cloaked figure. But then he has to account for where he found the time to alter their memories, and convince people he knows the False Memory Charm.
• That Dumbledore did it. Dumbledore just might go along out of guilt, and the Malfoys would go along to see Dumbledore brought down. But McGonagall would probably not stay silent, doubting Dumbledore's guilt and knowing Harry is an Occlumens.
• That Dumbledore confessed to him that he murdered Narcissa Malfoy. But that's a separate crime, so it doesn't save Hermione without a side deal with Lucius and Harry blew his chance at that.
• That Bellatrix Black broke into Hogwarts, tampered with Hermione and Draco, confessed to him to taunt him, and fled. Too many odd events, especially since Hogwarts is supposed to be hard to break into: Lucius would suggest it was Dumbledore Polyjuiced into Bella to set up Harry with a lie.
• That Quirrell did it and revealed it to him, as well as that he was the rescuer of Bellatrix Black, to show that Hogwarts couldn't protect his friends and in hopes of intimidating Harry to the cause of Voldemort. Bingo.

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.