What I'm asking is "is there a better process to inlet barrels into stocks that is more uniform, consistent and quicker that doing the job by hand as you have described above?"
This applies to solid timber, laminate and synthetic stock of barrel profiles from 1.25" parallel (simple) down to a no3. This is not for production but my time is valuable and I like doing things in an efficient way that can be accurate and repeatable and that's what I thought this site was about.
OK, as a guy who used to think that this could be automated to a large extent, but learned the hard way, here's a quick answer:
No.
Now, here's an explanation in three parts:
1. Good stock wood, especially maple or high-figure walnuts, will chip out if you come at them with a end mill (or ball mill) and think you're going to just run the mill up the side of the barrel channel. You can get a clean cut in low-figure walnuts (in my experience), but once you start paying $600 and up for a stock blank, and you start getting some nice figure in there, look out. If you do run a mill up the barrel channel, the safest bet is to just use it to rough out the barrel channel and leave anywhere from 0.050" to 0.125" on the sides of the channel to be cut off with hand tools.
Laminate wood stocks sometimes cut better.
Oh, and woods are abrasive, and will eat up HSS tooling. Use a good quality carbide ball mill.
2. Barrels only become true along their length with a bunch of work. Most people don't realize this, because they don't have well-developed eyes to judge these things. I cannot recount how many barrels for which I've paid extra money for the barrel manufacture to profile them that show up with dips, high spots and waves in the exterior profile of the barrel. If you are going to use these barrels as supplied, you will quickly find out that a barrel channel cut with a machine doesn't quiiiiiiite fit, or it leaves gaps. Not huge gaps, but gaps nonetheless, that aren't indicative of the highest quality work. When your customer is supplying you with a $600 to $1200 piece of walnut, they want perfection, not "close enough."
I have had to true up some barrels that were as much as 0.020 out of round with the bore. Some barrel outfits (I won't mention who) put some very junior employees on the job of polishing barrels on the belt grinder with the barrel spinner, and you sometimes get very junior-level results. I've had to take light finish cuts on a lathe and then strike some barrels for hours with a lathe bastard file, draw-filing it, to get it round and smooth again after someone who didn't know what they were doing "polished" it on a belt grinder.
3. A large part of your question is probably predicated upon you not having seen top-quality gun work. Most people have not. Modern mass manufacturing of guns has turned "free floated barrels" into an excuse to ship rifles with so much room between the stock and the barrel, you could fit a wad of currency around the barrel and run it up/down the length.
Last issue, which I forgot to mention:
I've used a mill to rough out barrel channels and receiver inlets. But I've only ever done that with a piece of wood that wasn't a rough-cut stock. I've done this only when I've had a pure slab of wood, with flat sides.
Most of what newbies don't understand about gunsmithing comes down to this: Gunsmithing looks easy on paper. Oh, you want to make XYZ? Put it on a five-axis CNC mill with the right software, and ta-da! Instant gun parts, made nice and cheap.
Well, that's a nice theory. I used to subscribe to this theory. Then I went to gunsmithing school, and started working on actual guns.
Here's what most people don't understand about using a machine tool (mill or lathe): You need to set up the part, and hold it, in a way that you can work on it, and you need to be able to indicate it in.
Sounds real obvious, right? OK, so let's talk about cutting the barrel channel on a stock blank and you don't have a truly flat slab of wood, or on a stock blank that doesn't have a flat side any more - because it's been rough duplicated.
When I mill a rough barrel channel with a carbide ball mill into a slab stock blank, I will use my Saf-T-Planer to mill at least one side of the stock blank (depending on how thick the blank is) to be as flat as I can make it, and after that, I'll put the stock blank into a joiner and make the top edge be as perpendicular as I can make it to the newly-flattened side. THEN I can put this into the vises on a mill and make a rough cut.