Small die grinder, dremel tool and a cutoff wheel. Cut the nut but DON'T cut all the way thru to the threads on the barrel. Make several cuts around the nut. Cold chisel and hammer, tap, tap, tap. Will probably break off. If you have gentle hands you could turn the cutoff wheel sideways to the nut and work it back and forth slowly and lightly. If there is enough tension on the nut it might crack when it gets thin enough. Have never done this myself but have 25 years as a heavy equipment mechanic and welder under my belt and have dealt with some of the most miserable p.o.s you can imagine. Patience is the key, especially if you are trying to save the barrel.

Another user suggested heat. If you've never done anything like this all I can say is good luck. Have to remember the barrel is probably heat treated in some way from the steel mill depending on what type of steel it is. To much heat and you change the grain structure, harden it, make it brittle. I'm no metallurgist but to much heat, improper cooling can affect the barrel and not in good ways.

In one industry I worked in we had a routine job where the nut would never come off, with a wrench so we used an air hammer with a sharp flat chisel bit. Angled it just right and hammered a few times, then moved and did it again. The sharp impact from the air hammer broke the nut loose easily.

If it were me, I'd use the die grinder and cutoff wheel or a burr bit. Steady hands, patience and nibble away at it slowly.