>>11856440
Don't have one of those, but just found a single video on youtube were someone disassembles one to try to fix the stick and was surprised to see they use photosensors (light sensors). Maybe the white undersidse of the tabs (light reflectors) at the bottom of the stick need cleaning?

The dude in the video did the exact same things you did but wasn't able to fix the sensitivity issue. He concluded that maybe the spring for the stick was worn out and not centering it properly, but he wasn't able to take the bottom of the stick apart, and it seems nobody on the Internet knows how to.