My hands hurt from the industrial screws and everything but I was able to look at the other controller, whose membrane was intact and good, and put it in mine.

Cleaned it all up from dust, put it back together and tested it.

It works. I feel vindicated! 🍊

Come to find out the membrane inside (this is an old controller) was busted where the A button was, leading to the sticking.

We had a lower end controller of the same brand in the house that had a busted trigger, so today I went at both to see if I could swap pieces.