A couple of other things to think about:

Soft case heads will result in popped primers. (The soft head expands too much)

A too long chamber will often result in popper primers: The cartridge walls grip the chamber upon firing, there is too much space between the case head and the bolt face, the primer moves back. Combined with a soft case head and the primer will fall out when the bolt is cycled. I would section a fired case and look for wall thinning just ahead of the web. If you find thinning, the chamber is too long.

Short throat, or a bullet seated out in the lands, will boost pressure and pop a primer. So, slightly resize the case neck a short distance, seat a bullet out too far, coat the bullet with prussian blue or smoke it, cycle the dummy round through the action and read the land marks on the bullet. You will push the bullet back into the case when doing his, and will know where the throat is for future seating reference. Might take a few tries. Watch for the bullet sticking in the lands when the bolt is opened, might have to size the neck a little more. If you stick a bullet in the lands, immediately take a cleaning rod and push it from the muzzle to dislodge the bullet. Last thing you want to do is leave a stuck bullet in the throat: If you forget it a few days later and chamber a round, the stuck bullet will push the other bullet back into the case, pull the trigger and blow up a rifle!!!

A chamber cast and proper measurement would tell me a lot.

If I had the rifle, and the above showed nothing wrong, then I would glue on a strain gauge and run some pressure trials.

Above posters may be on the right track, the cartridge might be loaded from the factory "on the edge" to obtain near 416 Rigby velocities. This is why I believe in big cases for a DG rifle!!!!