My thought: split the difference with some of your comments. Have a Joker of mysterious origin show up, but then lean heavily into the "dark mirror" angle. He's not just Batman's moral opposite, in many ways he's the anti-Batman: a brilliant obsessive polymath bringing to bare a vast array of skills and resources to enact changes upon the city. Only, since his founding morality is "amoral nihilism", the changes he is trying to enact are "Make the city a more anarchic land of crime and corruption, so I can sit as its king and do whatever I whim". He's not trying to sell some ideological point to the general public ( ala the Ledger Joker ), he's just trying to make the place more suited to his own use.
Perhaps have a scene with an almost literal "Joker cave", showing him having assembled his tools and gadgets, zany conspiracy boards across which he's plotted out his plans, stuff like that. Also, and this would probably be controversial: have him get committed to Arkham on being caught, and make clear that this is *deliberate* on his part. He's *not* insane, not in any criminal sense, he simply *chooses* to go there for reasons of his own ( facilitated via a mix of acting skills and corruption of the system ).