A couple of things I would try before I went to welding, etc.
As I understand a couple of teeth are left. Are any threads from the barrel nut visible? If you have enough surface simply use a pipe wrench to remove the barrel nut.
Since it is 'stuck' I would try to use barrel blocks first in order to ensure I didn't unseat the barrel extension. Otherwise, make sure your reaction rod is solidly secured.
You can make a set of barrel blocks easily enough -
* get two short lengths of 2x4, mate them perfectly together tighten them into your vise (alternatively you could screw them together);
* use a speedbore type (
http://www.irwin.com/tools/drill-bit...speed-bit-sets ) as close to your barrel diameter as possible and dril through the 2x4's at the joint - the speedbore screw end gets you started and holds in place until the larger cutting bit engages the wood;
Attachment 52409
You say there are a couple of teeth left on the barrel nut. If the pipe wrench won't work, drive the nut off. The receiver has to be solidly mounted for this, so I would probably use the reaction rod to reduce vibration.
If you have a piece of hardwood, I would use it against the tooth, otherwise use a large machinist punch. Make sure it is solidly mounted and that the punch/board is solidly against the tooth. Use a big enough hammer to transfer some energy and sharply rap - versus pound/beat - looking for an impact that jars with as little force as possible. You can increase the power of your blows as needed, but start with a sharp rap.
You'll get it.
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