TL;DR? See the bottom. I'm researching a fix for this. My Steam Controller's rubber thumb stick is also crumbling. The thumb stick just slides off the joystick. There are no fasteners or adhesives to worry about. If you pull it up, you'll see it slides a millimeter or two before the case gets in the way. I disassembled my Steam Controller today, and the whole thumb stick slid off once the front cover was out of the way. The same goes for other controllers, according to what I've read online. I just tested this with an old XBox 360 controller that I'm never planning to use again. After opening it, the thumb stick just popped off. The 360 thumb stick's dimensions are very close to the SC's. The hole underneath is almost identical, and in personal testing it fits nicely on the SC's joystick. The 360 thumb stick fails in two places. Both might be good enough, with slight modification. The head is slightly wider than the hole in the Steam Controller's case. I managed to force it through at an angle without...
Clutch belts are tight. There is a commonly available lifter tool to pull the belts far enough to remove and insert the beater bar. I would have been in trouble if I hadn't been able to makeshift a lifter with an L shaped hex wrench and a pair of vice grips to hold onto it.