Buzzard Bait,
I have a lathe, but I still use the ball lapping method. I came up with it probably the same way others have; when I was younger and short of cash, but shooting what little money I had up in matches, where I wanted a rifle that grouped as well as I could get it to. Since I have a lathe these days, I usually cut the muzzle square on it and do and outside chamfer on it, then go to the ball lap. When I was young and poor and didn't have a lathe, I scraped together money for one of the 90° cutters that Brownells sells and used that.
The reason I like the ball lap is that a sphere is self-centering over a square hole, and as long as the muzzle starts square, that center will be the bore axis. I've also cut crowns on the lathe, of course, but a right angle cut is the only one that doesn't require centering. So I can to that square cut on the 3-jaw chuck and it's good enough for the outside chamfer. To cut a crown, though, I have to center the bore in the 4-jaw chuck, and by the time I've swapped the chucks, turned a brass mandrel that kisses the rifling to get a smooth concentric surface to make indicating the center easy, and then actually adjusted to the chuck true, the ball lapping is done and is geometrically perfect. The result is also cleaner looking as it produces no tool marks.
I prefer the ball to the round head screws, because the latter usually are not actually round but elliptical in profile, so they don't truly self-center and depend on the fellow operating the tool to randomize the angle to a true average. Also, I don't like using something that only turns in one direction. That does produce scratchy looking tool marks from the removed metal balling up and scratching itself, where the back-and-forth motion I described for lapping doesn't make any. It's the reason engine valves are ground that way.
I've seen photos of M.L. McPherson cutting off and crowning his barrels at the range to tune them. Hacksaw, square and some files to get the end squared up. Glass marble rolled under his palm for a lap to cut the edge recess. Same self-centering principle.