Seems like the reports of removing smooth barrel nuts aren't exaggerated.

Started with the Wheeler barrel nut wrench. That thing is poorly designed, as it bends the screw when it tightens. Took some others' advice and went straight to grade 8 screws. Broke 2 of them so far.

Used a barrel vise but didn't want to mar the barrel, so wrapped it in a rubber inner tube. Couldn't get it tight enough to keep it from twisting. Cranked it down tighter and the vise body snapped in half! Doh!

Looks like I'll be heading back to the store for
A blue wrench (propane torch)
A pipe wrench if the propane doesn't work (I have a spare slotted nut anyway)
A new vise (NOT from harbor freight this time!)
Nothing like an excuse to buy more tools!