I've been following your project with a good bit of interest. I was distantly involved with a similar project. The original goal was to make a simple revolving .44 cap & ball carbine with a permanently mounted stock.
We wound up with three completely different carbines: a Walker/Dragoon, a '51 Colt, and (most successful) a '59 Remington.
The Walker came first. The smith chopped away the round part of the barrel, bored out the stub, threaded in a .45 barrel from some kit or other, dressed a forcing cone, and then started work on the other end.
The buttstock was even simpler. It was pistol-gripped, of course, with the back half of the grip irons replaced by stock-mounting tangs. The stock was supposed to be based on the look of a '94 Winchester but it wound up looking more like a stock from an M-79 Grenade Launcher. Ah, well.
The '51 Colt went better... at first. The barrel mounting was difficult-looking. Our mad machinist removed the barrel as a cylindrical section, removed additional material to allow weld space, arranged a pin jig to hold the barrel and mount stub in the proper relationship, and did the weld (MIG, I think.)
The stock went much better, and looked pretty nice.
The problem was that the cylinder spindle, frame pins, and wedge weren't strong enough in this case. Things worked loose pretty quickly.
The Remington was plain vanilla. Turn out the old barrel, turn in a longer one. Even the grip frame was untouched. The stock was fitted to match the grip irons on the left side, and an almost stock pistol grip was used on the right. Biggest mod on the grip was the two slightly larger bolts that held the two halves together.
My contribution? I scrounged up the (failed) '51 Colt and did the drawings for the tang castings used in mounting the Walker/Dragoon stocks.