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 don't know what the other side of this looks like, but if you could drive it with an impact driver on the lowest setting (assuming you used copious amounts of anti seizing spray), the constant hit from the impact driver is great at loosening stuff up. Also, try get painters tape between the wood and the domes head. Then flip it over, apply weight to the domed head by pressing it against your bench top (more tape on the bench top), and that gives a surprising amount of friction.