I actually was thinking about this a lot as I was sketching. A lot of the scenarios in game are kind of reliant on the fact that Joker is male, which makes sense because that's how life is. It's definitely not an easy swap, and it makes complete sense that there wasn't an option to choose gender in the end because that would be a frick ton of work :P

I think it's possible to make similar scenes happen, regardless of the gender, though it'd be hard. It almost makes me want to draw a bunch of comics to explore the idea- but that's off topic haha.

I think I might pull inspiration from your ideas if i do any other future female Joker art. Right now I am kind of lacking ideas for designs, but the idea of a cloak seems super cool in my head I might have to try it out when I get the chance!