It helps when you are attempting to inlet a swamped barrel that you have prior experience in BOAT BUILDING! Because of the curves in the hull of a boat, boat plans, and builders use " Stations" on both the plans, and on the actual keep or wood frame of the boat. In fact, most wooden boats space the ribs at the station lines.
On gunstocks, you want to use a long flexible ruler, that will allow you to mark the length of the barrel on the stock black at 1" intervals, for the most part. For the tight curves( bends) where the barrel is swamped, many builders will mark stations every 1/2" or even 1/4" on the blank. That allows you to take depth measurements on the barrel at each station, so that you an use a depth gauge to guide you in cutting the mortise to the right depth, and, eventually to the right diameter when working with a round barrel section.
To remove the waste wood, many builders will drill holes down the centerline to the depth marked on the ledger board they make up to transfer barrel diameters from the barrel to the stock. Some dispense with a separate ledger board, and just write notes on the side of the stock blank at each station indicating the max. depth.
You can buy router bits in about every size imaginable, to cut away the waste wood from the barrel mortise. However, the same work can, and was, done using saws, and chisels. Use a piece(s) of cut-off barrel, as a SCRAPER to get the mortise to the final dimensions. You can solder or weld a handle to these short sections of barrels to make the scrapers needed to take that last layer of wood off to allow the barrel to seat properly. :hmm: :hatsoff: