"It's all right, Gregory," Draco said, as gently as he could. "All you've got to do is worry about protecting me. Nobody's going to blame you for following my orders, not my father, not yours."
Hmm I wonder how much trouble they are in, they were supposed to keep Draco from harm and he almost got killed.
Well if everyone is right, you and I will be learning the lesson together.
Not Elizer, just Harry.
I'm sure I got many things wrong, the only thing I'm feeling pretty confident about is that Harry is going to frame someone else, and Lord Jugson looks like he has been being fattened up to be framed. The rest is just the story I came up with as most likely when figuring out how Harry could do it. I could be completely wrong, I could be right about the what and wrong about the how.
Perhaps I should have said 90% that my plan is the plan or superior to whatever Harry comes up with.
Yup that's what I should have said alright.
Go ahead and read the rest of my plot, I would say Harry has the best possible win here beyond overthrowing the entire ministry and remaking the government in his image. At least from Harry's perspective since he doesn't know that the real best win would be exposing and vanquishing Quirrelmort.
Hopefully I'm not about to learn a big lesson in humility, I would be less confident but I haven't seen or thought of any other plans that satisfy my criteria.
Basically the short answer is Harry used the time turner, invisibility cloak, and Quirrel to fake all of the evidence.
The long answer is, Harry waits until the end of the trial, goes back in time to the start of the trial and steals Lord Jugson's wand out of his pocket. He then heads over to the magical law enforcement department in the Ministry which is of course around the wizengamot. Harry knows that Quirrel is probably being held there for questioning since he didn't return to Hogwarts. Harry then steals the wand of Hermoine and Draco out of custody (or possibly heads over to St. Mungos to get Draco's wand from him there if it is there instead) and then finds Quirrell.
Using the invisiblity cloak and the time turner Harry goes back in time further with the defense professor tampers with all the wands to fake the spells properly either by using some spell, or just brute force recasting all the spells in its history far enough back that the tampering can't be detected. Harry then gets Fred and George to volunteer to be false memory charmed with the memory of Lord Jugson entering the Trophy room, and obliviated of the memory of volunteering. He then puppet masters it so that whichever Professor brings them to the trial shows up at exactly the right time. The defense professor returns him to the ministry, he replaces the wands of everyone involved a split second after they are taken in the first place and replaces the first Harry seconds after he goes back the first time.
Okay now some criticisms I have of my plan is that its hard to imagine why Lord Jugson wouldn't remain disillusioned the entire time. However perhaps Fred and George could say they used their wardbreaker monocoles Dumbledore gave them which allowed them to see dislliusioned people.
Another thing is that Harry could theoretically go back in time and get Dumbledore or Snape to fake the evidence instead but I think it would be more likely for Quirrel to do it. Quirrel is probably ambivalent over whether Hermoine gets nailed or not but he would have a motivation. The first way Harry develops a deep hatred of the Ministry and wants to overthrow it as he intends. The second way Harry still develops the deep hatred of the Ministry but sees Quirrell as even more of a valuable ally/mentor. Quirrel did after all prevent Hermoine from getting killed by the wizarding world establishment which Quirrel wants to overthrow. Lord Jugson could have some alibi but thats unlikely. Stealing and replacing Lord Jugson's wand could be tricky but certainly within Harry's power. Same with finding and freeing Professor Quirrell.
Above all I like this plan because it ends up with the best possible ending for Harry out of any plan I've seen. He saves the girl, regains his friend, and vanquishes a powerful enemy. He also does in a way that doesn't break the rest of the plot because things can go back to normal afterwards. The attacking Azkhban plan would completely destroy the rest of the in Hogwarts plots that have been set up, and freeing Hermoine on a technicality such as marrying her or trading in all of his Blood debts would still leave the magical world thinking Hermoine is a murderer and that Harry doesn't give a shit that Hermoine is a murderer. It also has the irony of fighting fire with fire, using False memory charms to fake someone else using False memory charms.