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:
A little super glue and a chunk of dowel, maybe?
Super glue is super fragile
My hand plane that was cracked in half that is currently held together via super glue disagrees