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:
If you're doing this type of stuff, I'm assuming you have some kind of dissolvable glue.
Protein based wood glue stops being glue if you add vinegar for example.
So use wood glue to glue a nut to domed back part of the bolt, or just throw a big glob all over the blot and saw handle.
Obviously make sure youve thrown a bunch of anti-seize on the other side first. This will stop it from spinning, but might not be enough to break it loose.
You could also try rigging something up with clamps and a piece of stuff rubber against the domed bolt to keep it pressed up against the inside of the handle.
But honestly?
Carriage bolts fucking suck, and you can just drill it out and find an era appropriate replacement. I grew up working on classic cars that always used them, and it's worth looking around to see if you can just buy a dozen to keep on hand. Depending on how old the saws are, I doubt they're original anyways.
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