Assuming a lever gun here.
1. Have PTC grind a hand turned piloted reamer with the external profile that you want. That will require you to provide the bore, barrel OD at the muzzle, and an accurate profile of the crown. Pros - no finish damage from a steady rest, etc. Cons - cost will be high.
2. Make a long mandrel to slip in the rear of the receiver with a driving lug mounted to a threaded hole on the side. Have to install the lug through the opening for the trigger plate. Mount in the lathe and recut as normal. Pros - inexpensive, do it yourself. Cons - damage to the receiver if you don't do it right, damage to the finish from the steady rest on the barrel.
I've done simlar when cutting down barrels on Mausers and it worked fine with careful prep and slow lathe speeds.
edit - The mandrel is made as large as possible for rigidity and just clears the bolt raceways. The end is turned like a center to fit the chamber end of the barrel. If the raceway is rectangular, then the part that goes into the raceway can be formed to match. There are ways to prtect the finish on the barrel from the steady rest, but I have no experience with that, so you'll have to get input from elsewhere on that one. I've never damaged a receiver doing this out of 20 or more that I've done.
