I just finished a gun with a 36" barrel, 28 ga., mounted on a Chambers Little Feller Stock for my grandsons ( 13 " pull, five pounds weight)
It came from Muzzleloader Builders Supply where the one inch breech fit exactly and the muzzle had to be bedded because there was about a 32nd of an inch difference and the octagon channel needed to support the round.
Of course that's not acceptable except for the fact that the gun was built from spare parts with a grandchild purpose, but for your purposes this thing gets tiny out by the front end
The Cartouche in the pictures is about 9" wide and , as said, the pull is all of 13" if that helps with proportioin.
Proportionally, this is different from the .62/20 Ga I ordered from Track for another project, being smaller with thinner walls at the muzzle. FRankly it became a case of who had what in stock, but they are all reliable barrel makers.
No, it doesn't have the same dimensions and I'd advise a chat with the Vendor before you place your order. MUzzleloader Supply installed the plug and I would ask the guys on this forum about soldering the lugs in lieu of the thin nature of the barrel versus heat management versus your experience level.
Don't shoot yore eye out, kid
The Capgun Kid
PS This little gun tickles me no end. I believe Mike said the one he made weighed in at four and a half, so I'd ask him for some pictures. It'll be a fun project when you settle on your decision.