So my original question in my original post that has remained unanswered after more than a page of posts was about the neck annealing and reaming.
I have never had to turn necks after necking down from 375 to 338.
I have to turn down my necks on my 338-416 Rigby Improved due to the huge difference from 416 to 338, but I also have a tight neck chamber.
Yes, I anneal my brass prior to fire forming AND necking down, but a word of warning, in some dies that do not have a tapered expander, an annealed case can crush the neck, so depending on this, it may be better annealing after the neck is reduced.
The issue with the neck increasing pressure is only partly correct. The neck releases the bullet early in the ignition phase of the combustion sequence, it only takes a little pressure to do this. If you don't believe this, then a simple test will show that even the pressure developed from a magnum primer is enough to expand the neck and release the bullet. If you prime a case and seat a bullet that is one cal smaller and fire it, the distance that bullet will travel is rather amazing and measuring the neck before and after will show just how much the neck expands just from that little test.
So, the pressure increase you are concerned with really is moot. I doubt you will need to ream or turn your necks, unless you have a tight neck chamber, which I doubt as it sounds like a SAAMI chamber and most of these have a .006"-.008" clearance in the neck anyway.
My only SAAMI chamber in my Weatherby rounds is my 270Bee, it has the SAAMI .376" long throat, all my other chamberings have the
.500" throat that Roy originally used and they are .0003"-.0005" over bullet diameter, which is tighter than most modern throat designs.
In fact, Roy's own original designs ran 1/2", 3/4" and 1" throats when they were still proprietary and had no SAAMI influence. In fact it was CIP in Europe who first recognised them as a factory offering.
Cheers.