Have you examined the patches? I have never been able to get 777 to work well with round balls. Even with a Wonder Wad under the patched ball. The patches were always severely damaged.

I suggest you try that barrel with a charge of real FFg black powder. I'll bet it will shoot better. I have totally abandoned the use of 777 with PRBs..... However, I have not tried "the cornmeal on top of the powder trick". That might insulate the patch enough to keep it in one piece.

New barrels often have sharp edges on the lands, and will sometimes cut patches until they wear smooth a little bit from firing PRB's. In addition, I would very strongly second nchawkeye's suggestion that you go to a fabric store with your micrometer and buy socotton pillow ticking of .020" or .018".

Thicker patching might make loading more difficult, but it might also improve accuracy.