I believe you will need a 378 Weatherby. You will be about 500 fps short of your goal with a 375 H&H and a good 100+ fps short with a 375 Weatherby.

You are looking to produce 20% more velocity than the standard so one would need to boost pressures 4% for every 1% increase in velocity per Mule Deer's rule. I doubt the brass can handle that kind of stress and I guess it would be pretty hard on the rifle too. I've shot a 378 Weatherby and I did not find it to be a pleasant experience. And it was a good 100 fps slower than the OP's desired velocity.

Last edited by woodmaster81; 06/21/20.