This method was presented by John Bivens in Rifle Magazine back in the last quarter of the 20th C. It has worked well for me and will for you too.
Saw out your blank including half of the barrel channel area. Be sure to include the radiused area at the breech...it is not a 90 degree cut! Mark a centre line at least down the barrel channel (I go completely around the stock and maintain that line during the entire build.)
Inlet your barrel's breech end without a plug to butt up against the end of the barrel channel - very little wood needs to be removed to accomplish this. Now clamp the barrel to the wood at the breech and muzzle, and add a clamp in the middle too.
You will need two steel rails for the next part. I used two lengths of 3/8" key stock (cold rolled mild steel) long enough to do a 48" barrel. Drill holes as close to the outer edge as you dare to allow dry wall screws to pass, 3" or 4" apart for the whole length of the rails. Be sure to drill the first hole in each rail 3 1/2" - 4" from the end of the rail so that the screw that goes through that one into the stock does not leave a scar that will involved the lock molding. At the mid point of the rails drill additional holes between each of the holes so that there are holes 1 1/2" - 2" apart for the muzzle end of the barrel. Grind a radius on the breech end of the rails to allow for that part of the wood that has been sawed to that shape. While you're at it, make a centre punch out a piece of drill rod or a nail, that will also just pass through the holes. There is no need to countersink these holes.
Lay the two rails alongside the barrel on the stock with the butt ends adjacent the breech end of the barrel, and clamp the rails to the sides of the barrel with as many small C clamps as required. Using the centre punch you just made, punch each of the holes. Using a drill bit that is a tad smaller than the major diameter of a drywall screw, in a hand held drill, drill a pilot hole in each of the holes deep enough to take the entire length of the screws. You can use any type of screw here that suits you, but the dry wall or gyprock screws are small diameter, have great strength and bite and are cheap and ubiquitous. Screw the rails down to the wood.
Now lift the barrel off the stock from between the rails. What remains is a perfect facsimile of the barrel. Now it is time to make another tool.
You need a back saw that will slide along the inside of the rails to cut straight down to the depth of the side flat of the barrel. I used a section of a rip saw to which I attached a handle so that the saw cuts on the PULL. And I removed the set from one side of the blade so that the saw only cuts straight down and doesn't undercut. I scribed a mark on the saw indicating the half barrel flat mark so that I didn't cut too deeply. The half way mark is taken at the swamp of the barrel or the minimum dimension. Start at the breech with the safe-side of the blade against the rail and draw the blade down the stock. In short order you will have a cut that is perpendicular to the top of the stock and full depth of the side flat. Reverse the process now and start at the muzzle with the safe side of the saw against the other rail and repeat the process. The rails have now come to the end of their usefulness, and can be removed.
With a felt pen, make a series of lines across the barrel at regular intervals, ie: every 4" and transfer these marks to the wood using a pencil. Now measure the diameter of the barrel at each mark, and divide by two to indicate how deeply you need to make your barrel channel at each mark. I include in the measurement, the thickness of a steel scale that I lay across the channel and which is the stop for the Vernier calipers I use to measure the depth as I proceed to remove wood.
From now on, it's simply a matter of taking out wood to accommodate the barrel. I start with a large flat chisel and take out the slivers of wood that butt against the side flat. Be careful with the chisel not to cut past the vertical cuts as this will weaken your forestock. Then I use a gouge and a mallet, starting at the breech and watching the grain direction as I take out big slices of the channel wood. Stop often and measure to ensure you are not going in too deeply.
When you are within a few thou of the bottom of the channel, switch to a bunch of flat chisels to cut the bottom flat, keeping in mind the width of the bottom flat as it narrows toward the swamp and flares again at the muzzle. The angled flat is also cut with flat chisels though I find skew chisels often work well here too.
At some point, when you are very very close to getting your barrel to full depth, you will want to resort to scrapers. I use a wad of towel and inletting black to help me find the high spots, and use it as sparingly as I can. Too, you may have to scrape the side flats (cut only with a saw) to get the barrel to drop down into the channel. I take my barrel down so that it is about 1/32" below the wood at the breech.
At this stage, I take the stock to the bandsaw and slab off the wood down to the screw holes. Be sure to stop at the rear-most hole so that you don't remove wood where the lock panel is to go.
An option is to use a very sharp large flat chisel to clean up the saw cuts while the steel rails are still screwed down to the wood, but care must be taken not to undercut the side flats. Also, other tools, such as special planes can help to take away all that wood. But I personally use chisels. The whole process of inletting a swamped barrel takes me around 5 hours I think. I use the servises of David Rase, Mark Wheland, and Mark Weder mostly now, but for tapered barrels and half stocks and pistols, this system is stellar.
