To keep the barrel from turning in the vise:
If your barrel is tapered, but the vise jaws are parallel, you will need a tapered shim or a set of maple inserts that fit the octagonal part.
Sprinkle the barrel with rosin, like violin rosin, for a better grip. The vise must be TIGHT. When you start leaning on the wrench, watch ththe barrel, to make sure it's not slipping.
To keep from buggering up the top flat of the breechplug:
I put my wrench on the plug from the underside. I don't let the tips of the wrench jaws go past the top finished surface of the plug. Inspect your wrench jaws to see that there are no burrs. File and polish any rough spots.
How many originals do we see with pipe wrench marks, toothy jaw marks, buggered up plugs, etc? Almost all original guns have been chewed up, probably for lack of a good vise.