I dunno if this is a terrible idea or not, but I would just make Peacock's grab super a standard super. For example, you activate it, super flash, she wiggles her fingers a little bit like with Lonesome Lenny, then she does her grab animation and if that hits, she does her level 3 super. No need for new assets. At least, i don't think so.
For Light Teleport, does that really have any notable difference to her Medium teleport outside of distance? I imagine if it were faster she could maybe use it in her combos to cancel recovery once per combo, but then she'd probably need to take a damage nerf either on use of the move or in general. I can only imagine how some people would freak out over a general nerf, though. Alternatively you could make it throw invincible (during all of startup at least). Only reason I really bring that up is that if your opponent calls jump and tries to Anti-Air throw instead of your predicted ground throw, teleport brings you below the ground, not over it. A few times my friend would use M or H Teleport when I called a jump and thus he would dodge under A Train. It has the benefit of not being aerial and thus not being weak to Anti-Air, so if L Teleport was throw invincible it means that at close range you have a method of avoiding ground throws that is safe from anti-air throws. Which, come to think of it, is about the only reason I can think of to use throw invincible moves.
Edit: I mean L Bang staggers, but it's probably one of the only throw invincible moves, that's not a command throw, I can think of that has another use? I dunno if these are good ideas anyway, but I think more ideas is better if it means a good idea eventually comes out of it.