I've used JB Weld around the house to permanently fix things that weren't supposed to break, and the stuff has held up. Bicycle handle bars that kept slipping in the neck, wooden handle that slipped out of a marble rolling pin, metal hook on a wooden board, plastic parts to metal parts, wood on wood; the surfaces didn't matter. Once it set, you were not going to get it apart. JB when mixed is about the consistency of thick peanut butter, and stays that way for five minutes or so. After that, you better have the pieces where you want 'em. Cause that's where they're gonna stay.
Mix two globs half the size of a dime together and apply it with a toothpick. That will permanently fix the recoil pad to the plastic plate.