Took it apart and cleaned it, put it back together and all seems fine. The Vol+ doesn't stick anymore, and the other buttons I've tried are working fine.

I have a couple residual questions.

What the heck is the window defogger trick?

There was a greasy residue on the side of the board facing the button membrane. Is that some kind of grease applied at the factory to promote conductivity? Rather than clean it off using a solvent, I just wiped it clean with a paper towel.