With a plan this complex there are many variables, so I just filled in my favorite guesses such as the person being framed, the order, etc.

Harry realizes the plan in that moment of desperation then gets the vote stopped to admit new evidence. He then presents to the court the testimony of George and Fred Weasley who say that during the night of the attempted murder they were out of their bed pulling a prank, when they saw Lord Jugson entering the Trophy room. They thought it was strange but since they were out of bed pulling a prank they didn’t want to tell anyone, until they realized that morning it could be connected. They then went straight to a Professor who brought them to the Wizengamot, and they repeat their testimony under veritaserum.

Lord Jugson claims they were false memory charmed, but Harry responds to this by saying that if you are so confident of it why not let us examine the last spells cast on your wand, and that of Hermoine’s and Draco’s? After all you have nothing to hide. Lord Jugson agrees and hands over his wand, and then priori incantum reveals to his shock that his wand has been used recently to do the imperius, obliviate and the false memory charm. Hermoine's wand has been faked to use the Blood Chilling charm but Draco's has no evidence of a duel past the army fight on it at all.

Harry explains that Lord Jugson in a fit of rage at Draco for losing to a mudblood and Hermoine for beating him made a plot to punish them both after the army fight. He disappeared after the fight, and remained in Hogwarts to imperius Draco to challenge Hermoine to a duel at midnight. Then he either simply stayed in Hogwarts until midnight, used a secret passage or apparated outside the wards and flew in a broomstick, or used the floo network to enter Hogwarts right before midnight. He made his way to the trophy room, stunned Draco and Hermoine as they entered, disillusioned them all, and took them outside of the wards of Hogwarts to do the obliviation and false memory charms returning them after the deed was done. Lord Jugson won’t have an alibi for the hours of 11:30 to 12:30 as everyone in his household would be asleep at the time.

He used Hermoine's wand to cast spells simulating a duel followed by the blood chilling charm figuring that when Draco died he could prompt an investigation into her which would reveal the evidence on her wand combined with veritaserum to convict her. He obliviated Draco and false memory charmed him as well just in case Draco was discovered, but he didn't bother to tamper with Draco's wand figuring no one would have a reason to investigate it, and the wands show this.

Harry further explains that Lord Jugson decided that Draco had become too friendly to mudbloods and was no longer fit to be a leader of the blood purists. By killing him after his public showdown with Hermoine he could get rid of Draco, Hermoine AND set his own son up to assume leadership of the blood purists now that the Malfoy’s had no heir. After the plot ended he obliviated himself (if he isn't an occlumens) to safely hide the plot forever. Lord Jugson is sentenced to Azkhaban, by Harry invoking Lord Malfoy's blood debt to Harry to decide the sentencing, Hermoine is freed and the blood purists lose face politically for wanting to kill an innocent girl.

In my next post I will explain how Harry did it.

For an optimal solution Harry teaches his enemies that poking him with a stick is very dangerous, and manages to turn this to his advantage by harming an enemy.

I'd just like to note that even then, Harry comes out the loser from this whole chain of events. Most importantly, he loses Draco as an ally, and suffers from knowing he hurt Draco's relationship with this father. Less importantly, Hermione has been psychologically hurt (I'd say traumatized), and won't get any personal redress. Finally, if Harry sets someone else up, he will lose the ability to expose the true culprit in the future, if he learns who that was, and so loses a powerful avenue of action against that culprit. The true culprit (or someone else) may even find proof of Harry framing Jugson, and then blackmail Harry with that proof.

The only way Harry could come out genuinely ahead is if he found and exposed the culprit, rather than frame a random enemy. Including scenarios where he could delay Hermione's punishment, or cancel it using blood debts, so that he'd gain time to search out the real culprit.

I believe a major psychological reason for people proposing so many theories for Harry's solution, some of them very impractical, is that they have an "intent to kill"; they don't want to propose a solution that settles for second best, like yours. They want Harry to win.

That sure is a lot of burdensome details.

Its the only solution I've seen that proves Hermoine innocence AND gains Harry an advantage. I think it was foreshadowed back in Self Actualization.