Let me set the stage first. For a bare minimum solution Hermoine has to be proven innocent so she can return to school without someone trying to kill her to score points for Malfoy. 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. But in no way is any solution good enough if it doesn’t end up with Hermoine proven innocent to the world.

He has a time-turner, an invisibility cloak, possibly the blood debts of everyone who claimed to be imperiused, possibly the wands as evidence, a very analytical mind that is currently very open to ‘dark’ ideas, and multiple people of different skills/motivations that he can coerce or get to help him.

Lord Jugson is someone that really doesn’t seem to have much a point in the story so far. It makes the most sense to me as someone who is being built up just to be the scapegoat. “"It would be justice for his past crimes, and I'd only do it if Jugson made the first move. The point isn't to make people scared of me as a wild card, after all. It's to teach them that neutrals are perfectly safe from me, and poking me with a stick is incredibly dangerous."” Also, The boy smiled, now with a touch of coldness again. "Okay, I'll figure out some way to set it up so that it looks like Lord Jugson betrayed his own side."

A big gaping hole like introducing the wands for evidence is far too obvious for Harry to pretend it doesn’t exist anymore, so that is avenue worth approaching. However Cloak and Hat is far too clever to have forgotten to doctor the wands, unless he deliberately wanted the wands to prove.
It would also be just like Harry to use the enemies tactics against them, and so the idea of thwarting an evil plot based on false memory charms by using false memory charms to thwart it would be appealing.