You have decribed the process exactly as it is performed.
16 yards, light loads, Move, mount shoot. Average the patterns, adjust the try gun. Repeat.
Here's the hitch.
I found I could not do it myself.
There were too many deficiencies in my mount due to years of adaptive shooting. Ie, neck craning, head tilting, hand sliding, face jamming, etc. 100 different shotguns I adapted to, rather than their stock to me.
Once we worked out an adequate mount, we could then adjust the try gun to more consistently place the pattern where I was looking.
It was money well spent. Every stock I have that is equal, or close to, the measured dimensions is consistent, and pleasant to shoot.
I say this because I know of no way to observe all the little deficiencies without a trained, experienced observer watching you shoot.
Ultimately, my least consistent element has been cheek pressure. It's been very difficult to feel the right cheek weld during the mount on a wild bird's flush.
The process is not difficult, the observation skills are.
Just my two cents.
Oh, and the process doesn't really apply well to people that shoot alot of skeet targets premounted, whether registered or fun. They look at the bead, and measure, which is exactly opposite what is being preached in a fitting. It's a very tough habit to break. Going from sustained lead to an instinctive mount.