YOu are talking about removing only 1/16" of wood, half from each side of the barrel channel. I would use a scraper to remove this small amount of wood, slowly working my way down into the channel until the scraper rides square to the bore the entire length of the channel. That is only 31 thousandths of an inch of wood to remove off of all the flats, and sides.
I might build a jig to guide the scraper so I don't move from one side to the other, but that should not be very difficult to do. As you go, insert the barrel to check to see that the new channel is straight and true to the original channel. Of course, this could be done with router mounted in a table with a guide bar in place. My only problem with using a router is the set up time would be extensive, and you don't have any real room for errors. You either have the guide set exactly where you want it to be, or you take too much wood off that stock. Yipes!
