I’ve used Peterson brass for years without any problems though I do not have any 338 I do use it across three different calibres.That probably would have been the typical path but after trying this/that/reaming/swaging I feel like I signed up for the ride, its completely possible that its something I'm doing wrong.
I did a bunch of pin measurements, these pockets are 0.209 dia x 0.128 deep. So no mater the primer they are of a usable size. I'm having some doubts about my press's ability to get things seated flush (feels like its bottoming out.
That could be be due to my 45-70 shell plate converted to 338LM (because a 338LM doesn't exist), shell plate isn't holding it tight enough to the press. I bought a shell holder for 338LM to use my RCBS bench primer but its MIA
I did find a major malfunction and the reason they've been hard to chamber, some dummy seated them 0.060 into the lands (DOH). Bullet comparator and print math got me close but the old jamb test showed I needed some more.
The running theory is I'm crushing not flush primers when chambering. I've pulled bullets on previously seated rounds and the primers have been igniting.
So I have a stack of the corrected bullet seating depth rounds to test.
I've crushed primers- these are not getting that kind of force.
I always have primed them with a 21st Century priming tool and not on a press as the tool makes it easy to adjust seating depth rather than going by “feel”… Quicker as well…
Perhaps that would solve your issue as you mention that the shell holder you are using is not correct for the case but a modified one and not allowing the press to fully seat the primers.
Just a thought…