Barrel in "padded" vice. (Nut wrench on barrel) SMACK the wrench with a steel hammer. The SHOCK of metal to metal from the hammer hitting the wrench will brake the nut loose.
No need to tighten it back up that much. You may want to change it again in the future.
Havn't used my action wrench since the first time I had to back it off when the barrel wouldn't turn. Maybe rear action wrench?
Try the "steel on steel" and see what that does. Worked on the last half dozen barrel changes I've done but I make it a point NOT to tighten the nut up that much. You can also use channel locks (padded) to hold the action for the first time braking the nut loose.
After that, hand hold works good.