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:
Carriage bolts are the worst, for sure.
I agree, drill it out, keep some replacements on hand, and always reassemble with anti-seize or the weakest loctite (they make some for just this situation, to prevent nuts from seizing but also be easy to remove). Hell, even blue loctite would work, as it breaks down with just a little heat.
Drilling a spinning bolt is Not Easy. Not impossible, bit there's better ways to go about things