What H53EXPERT said... Sometimes you need an "assistant" to keep the wrench pushed against the delta ring spring.
Plus some advice: put the whole upper in the freezer for 30-45 minutes, NO MORE than 45. Take it out and immediately put it in the vise and work on that nut. Steel (the nut) and aluminum (the upper) have different thermal characteristics, so the upper should contract a bit more quickly than the nut, which will give you a little better opportunity to get the nut off. And use the longest breaker bar you can on that barrel nut wrench.
If your barrel doesn't have a pinned muzzle device, you may want to just say to heck with the barrel nut and get a plumber's pipe wrench. After breaking at least half the teeth off of one nut, I gave up, borrowed an 18" pipe wrench and it came off with my first try. Of course you have to be able to remove the FSB to be able to change out the nut, so make sure your muzzle device comes off too.