Consider a 375 Ruger. I believe that it is very popular with guides in brown bear country.
I have both a 375 H&H and a 375 Ruger, and if I could choose only one of them it would be the Ruger.
The 416 is a heavy hitter but the 375 is much more versatile. There is good reason that the 375 is legal for elephant and cape buffalo. It works.