I'm thinking of going with or at least starting with this version of the Joker's origin, mixed with going under the name of the Redhood for his crimes if you don't mind.
I realized that if things go according to plan, Batman will have hurt/disfigured two people by accident–the Red Hood (with the chemicals and whatnot) and the Black Mask (he like, pushes him into something hot while Sionis wore the mask Andy it burned into his skin)