Ok, I've lost one of my buttons, they're on back order, and they cost $7 each. I went and bought some rubber cement, but was leery of using that as I don't want to irrevocably damage anything.
Went to Ace Hardware, was describing what I needed, guy suggested pipe/teflon tape. I'm trying that right now. I take a 3/4" section, double it over, put that down over the shaft, and screw the button down. Doesn't seem like it's going to go anywhere.