As a person who always does it that way, I have a few tips.
1. Use some tape to mark the average side wall depth on the saw you use to cut in the side wall, and cut no deeper than that anywhere. By the way, a shortened dovetail saw works best here as dovetail saws are sharpened rip, which is what you want for this cut. Remove the set from the guide side of the saw. You still want a set on the opposite side of the guide.
2. Be careful chiseling out the wood inside the sidewalls such that you cut completely through to the sidewall and not tear out a little wood below your saw cut. If you don't understand what I am getting at here, the first time you do it, you will. Of course, you don't want to gouge out a part of your side wall either. Just be careful with the chisel and make sure it is sharp. If you mess this up, don't worry too much. It just means you will be missing some wood under the oblique flats in the middle of the barrel channel which really shouldn't cause a functional problem.
3. Take a large flat chisel and make sure the sidewalls are trimmed square with the top of the stock BEFORE you remove the barrel guides. That way you can be sure the barrel will drop in the inlet without hanging anywhere. This will save a LOT of time picking at the tight spots that can be hard to find.
4. Two 3/4" gunstocking planes, one reshaped to an octagon profile will greatly speed removing wood in a plane. A gunstocking plane looks like a moulding plane but has parallel shoulders on either side of the blade. The shoulders are tapered in on a regular moulding plane. Cut with the grain.
5. You only need the inlet tight at the breech and muzzle so as to firmly hold the barrel in position in the stock. Don't obsess about the channel in the middle. Close is fine.