You can do swamped barrels with a router if you have a very finely adjustable fence (like the old micro-fence, don't know if they're still made) and you (1) cut the top of the stock to match the profile of the bottom of the barrel, adjusting for the total depth of the breech, and (2) cut the sides out to the max width (plus a little) of the side panels, and cut them to follow the profile of the side barrel flats. With a micro fence with a short (@ 3-4") fence guide and using a combination of square/vee bits, and running the router both ways (off both sides), you can get remarkably close with very little hand fitting remaining. If you're doing barrels with big breeches i.e 1 1/8 or so, you'll need router bits with sufficiently long shanks to safely be mounted in the router with sufficient length still in the collet.
Alternately you can do it by hand and take quite a bit longer.
Alternately you can pay one of the barrel inletting guys with the proper machinery for it, and wonder why on earth you didn't pay them to do it sooner!