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:
Ahh I get ya now.
In that case I'd do what others have suggested and glue a socket to each side and use ratchets to undo.