I'll tell you a trick we used to use in the aerospace business. Extreme cold. We used liquid nitrogen, the extreme cold actually shrinks the metal. I know you probably can't get any LN, but this works pretty good instead. Add several oz of alcohol to the barrel and add dry ice chips. After this soaks for awhile, empty everything out and add heat from a propane torch. The contraction/expansion might do the trick.
It is probably a given that the plug will be destroyed while your are trying to get it out, regardless of the method. Have you contacted Winchester or Brownells to see about a new one? Call CVA and ask out theirs as a replacement. A machinist can remove it and chase the threads pretty easily.
Good luck.
I like the thought behind this idea. My only question would be, would this change the temper of the steel on the barrel at all? To me, doing something like this on a gun would make me nervous to shoot it the following time, as I would wonder if the steel would be more brittle. Just asking out of curiosity more than anything else.
Like Hilltop said though, I would seriously just consider a new muzzleloader, especially if you end up going the machinist route. By the time you pay him and order a new breech plug, you'll be at least half way to a new muzzleloader.
Either way, good luck and let us know how you make out. It is always good to find out new ways of removing stuck breech plugs.