I suspect the serious muzzle rise that you describe likely has to do with the stock design along with how it fits you. It may be how you had the rifle supported at the bench. I also believe the most felt recoil you will ever experience shooting a rifle will likely be shooting off a bench.
All things being equal when you go to the bigger bores you do experience more recoil, however the .375 isn't known for sharp recoil or sending the muzzle to the sky on each shot. For the level of performance offered by a .375 it tends to push rather than smack you, and is rather comfortable to shoot. I used to teach bear / rifle safety in Alaska. Put literally 100's of folks of all sizes and experience levels thru the training, which included some amount of live fire and speed / accuracy qualifications. We used Winchester Model 70's, Remington 700's and a few Interarms. I don't recall any of the students having problems with muzzle rise. Big difference here is none of the shooting was off a bench.
Suggest you find a range where you can shoot your rifle bagged, but in the standing up position. If that doesn't help, find a friend with a .375 and see if their rifle gives you the same recoil problem.
Good luck.
Silvertp