My working career was in the manufacture of aircraft structural components. I did some of all of it. Starting in the machine shops, then Numerical Control, about 10 years as a Tool & Die maker, then I rode a desk in engineering data management.
I listed this background to maybe add some weight to my next statement. First telling by engineers, then toolmakers. After that it's hard to find someone with knowledge on the subject.
"3 full threads deep and maximum strength has been reached."
I personally never tested this, preferring a half inch or so depth.
But if this is true then a breech plug 3/8ths deep is plenty strong enough.
If anybody has ever heard this, positive or negative, please share.