I'm trying to make some 375 H&H brass out of 416 Remington. I ran it through the 375 die and trimmed it back to 2.850. I did get a few small dents in the neck but nothing bad. It still won't chamber in the 375 rifle. I didn't mess with my die setting from my normal use for 375 brass. Has anybody had luck doing this? I'm only doing this because 375 is hard to find and stupid expensive.

Maybe anneal it first?
Thats a lot of shoulder to compress back to the 375's long narrow neck.

Annealing is a good idea for the neck and shoulder,
maybe try graphite powder or a smidge of Imperial Sizing Wax if the lube is contributing to dents in neck/shoulder area.

But can't anneal much below shoulder,
and you may have the harder and springier lower case wanting to spring back as it comes out of the die.
Ouch.

Size one repeatedly and see if you can get it to chamber, being sure it is trimmed.
The cases may be growing in length enough with the diameters reductions to interfere with chambering.
But you did say you trimmed to max length of 2.850", eh ?
Maybe try trim-to-length of 2.840" then let cases sit overnight to see if they slowly grow in length or diameter after that prep.
Sometimes a re-sized jacketed bullet does.

It appears that annealing did the trick. With a test sample of one it set the shoulder back enough and not dent the shoulder. Various measurements around the case appear to be the same as the 375 case. This is the first time I had to anneal a case so I will do my research on how to do it correctly. Thanks for the help, this will save me the frustration of finding 375 brass.

Midway has Nosler over-run 375 brass right now for a buck something each.