Most of the nuts came out with minimal force, but the last one just spins in place. I tried rubber gloves, painter's tape, and duct tape to get a better grip. I'd rather not cut a slot in the domed nut if there's another good strategy.
The rest of the restoration underway:
I just rewatched Community, so read that comment in Keith David's voice...
https://www.youtube.com/watch?v=E_iqm7S-CwU