I had 2 375 H&H with different chamber sizes. Had several incipient case failures when I was not segregating brass to rifle.
Once I kept brass segregated and sized brass to rifle had no more case failures.
375 H&H case is prone to stretch due to the taper of the case. One of the reasons I sold the 375 H&H and went to the 375 Ruger.
My large chamber Savage 99 in 250 Savage has same issues in a tight chamber bolt action, long brass life and less trimming.
In my large chamber 250 Savage I create a false shoulder and fire form 22-250 brass to have it fit chamber on first firing.
Would be much simpler to have a proper size chamber.