One change that would help a lot is to enable the use of the parry as a reversal. With reversal windows, you can buffer batman's and KF's parry. This makes parrying between strings a hell of a lot easier (I can land it 9/10 times). With Joker since you can't reversal it, you really have to time it to the frame. While you can learn the timing, some parry windows are legitimately like 1-2 frame windows, e.g. GL's b+1,3. 1-2 frames doesnt sound horrible and since it is a consistent timing you should be able to muscle memory it, but I don't think you can plink in this game so its even more difficult.
The other changes you guys mentioned seem good as well. A holdable parry/increased active frames would help alot, or just being able to parry air attacks. Maybe if he could mb his parry to get a full combo, Grundy can mb his for armour.
Random stuff. b+2 is a decent move when close to the corner. Its only -1 so it is safe. And with the 2 frame parry, you can't just push buttons (risk reward is mega out of your favour though). In the corner, the knockback is less too. (Animation is sick too like Cat mentioned)
Also, what do you guys think about making crowbar safe? Its a slow advancing special that gives a hard knockdown. I don't see it being insanely overpowered. It would help with his mini corner vortex thing, since off a crowbar knock down in the corner, you can force stand up with b1 and standing 3. If crowbar was safe (or even positive) it could be a 50-50 in the corner based on the knockdown. If they guess wrong and try wake up, b+1, crowbar will reset the situation where you have to guess again. If they block low waiting for the b1, you can safely get the crowbar off and force the situation again. Seems really stupid since its like a one hit/two hit combo vortex, could be something. I feel the gimmicky teeth stuff in the corner will lose its impact as people get used to blocking the teeth and jump ins.
Edit: I realise you can fuzzy guard, but because of wake up timings, you need to commit to the wake up attack. b1 will beat this so you can get the crowbar out. If crowbar was safe/positive, there could be a legitimate mix up here.
Maybe there are other options though since you can otg off a crowbar knockdown with b1, standing 3 and d2.