GC,
I think most of us have had similar things happen at one time or another.
Either with shotgun chokes, Dan Wesson barrels, or the like.
One of the methods I've used in the past was to insert the choke/barrel nut wrench in the barrel as if you were going to remove it normally.
I then (depending on the gun) placed the muzzle with the wrench inserted, directly against the side of my bench. With the wrench handle up where I could give it a whack, and holding the gun muzzle tightly against the bench, I'd do just that, and after a sharp tap or two, it'd usually come loose.
With a shotgun length barrel, it was better served to leave the barrel on the gun and have someone else push the muzzle (with wrench in place) against the bench while you tap the end of the wrench.
If I thought that it was going to be "iffy" at best, I'd heat the barrel end below where the bottom of the choke's end sits inside the tube, and with the muzzle pointing up, allow the heat to travel through it's normal path, upwards through the barrel. This will (at first) loosen the barrel's grip on the choke tube, but if continued for any length of time, it'll transfer to the choke tube as well. Apply a goodly amount of heat, and then immediately immerse the muzzle end into a coffee can half full of penetrating oil. Oil high enough in the can to completely cover the choke and threaded area of the barrel. Light penetrating oil only...no regular oils.
The heat will draw the oil up into the threaded area of the choke, and with the other method mentioned, or between the two, hopefully you'll have some luck there.
Working as a mechanic most of my life, I've used this method on everything from ball joints, to stuck screws and guns. Sometimes it takes a couple of shots, but it'll work.
Good luck,
Bob