My reasons for assigning ~0% to some of these:

threaten to destroy Azkaban destroying one of the Dementors

They would lock him away to protect the Dementors who are Britain's most powerful magical weapon in reserve in case of war with another magical nation. (Quoth Dumbledore.)

offer the Wizengamot Voldemort's true identity (Quirrel)

Harry doesn't know that fact, so he can't offer it. Anyway, how would it help to reverse the judgement against Hermione?

using the Time-turner to alter Hermione's testimony to something easily falsifiable

Can't use it to change what's already happened. Hermione has already given her testimony, and Harry didn't even listen so he wouldn't be in a good position to subtly modify it. And the Veritaserum on her is already wearing off, precluding further testimony.

using the Time-turner to smuggle Hermione out under the Cloak

Harry and Hermione can't be both under the Cloak at once. People under the Cloak can still be caught by physically feeling around. The Aurors would stop them (certainly the one who wasn't under the Cloak at the time), and if they didn't, Hermione would be running around the building Cloaked but with no real way out.

ask for a trial by combat

Wizengamot would have to vote to make the trial-by-combat's results binding (otherwise why should it reverse the standing Wizengamot vote to punish Hermione?) Lucius will ask them not to vote so, because Dumbledore would be Harry's champion, and so they won't.

More generally, if Dumbledore could challenge Lucius to a duel every time a vote went against him, he'd have total control of the vote outcomes by virtue of being undefeatable in combat. And we know that's not the case.

have Quirrel make Bella confess to the crime

What would be the explanation presented for why Bella comes forward to confess, without implicating Quirrel? Just "Voldemort ordered me to do this and then Obliviated me"? Everyone would suspect Voldemort also false-memory-charmed Bella into believing she did it. And why would Voldemort sacrifice his most trusted and powerful lieutenant, whom he recently rescued at great risk, and not some smaller pawn? And why would Voldemort execute a plan to murder Draco or to frame Hermione in the first place? And how would Bella have gotten into Hogwarts without the wards detecting it, or Dumbledore's Map? And how could she be recovered enough already (if she appears to testify everyone will see she's not very recovered yet)?

And to begin with you'd have to explain to members of the Wizengamot that Voldemort is still alive and that he broke out Bella from Azkaban. Imagine the panic - no reasoned debate would be possible after that. But without telling them this, how to explain that Bella is turning herself in, and that she has been Obliviated of everything during and after her escape?

Oh, and by inspecting Bella they will notice she does not in fact have her Animagus form again, which will cause Dumbledore to rethink some conclusions... (Edit: she has probably regained her Animagus form on Quirrel's instructions, it would be stupid not to. See below.)