Have you tried using a button wrench?
I have, with limited success. When I really want to get these tightened down, I've used channel locks/vice grips. It seems that after a while, somehow, they can come loosened a bit. (It probably wouldn't be as annoying if I didn't have vinyl decals on the push-buttons, and if I wasn't so anal about everything staying perfectly straight.)
I imagine hot glue would be useless and superglue would be very permanent (and potentially very messy).
I was considering tightening the push-buttons down initially, and then adding a drop of superglue in two or three spots - nothing overly messy, but as you point out, this would be a very permanent solution. I could do this, however, if they ever got loose, I would likely have to destroy the threads to remove the push-button and then remove it. (Not necessarily a deal killer, if it works.)
Plumbers tape requires multiple rounds to be effective. Tip: always apply the tape clockwise when viewed from below (to match the screwing action).
I was thinking about that. Maybe I was just premature about the lack of tape I tried. It was a solution I tried pretty quickly, so maybe it deserves more scrutiny.
I also just thought that perhaps I tighten the push-button, and add a round or two of black electrical tape to surround the threads and the nut. Maybe that would be enough to stop it travelling and loosening up.
Thanks for the ideas, and the tip regarding the plumber's tape!