I'd be looking at a cartridge/caliber with better commonly available long range bullets rather than upping the powder capacity and the recoil.
The 375's are generally all twisted to toss the 300 Hornady BTSP, Sierra BTSP and the 350 gr. MatchKing or a 410 Berger which will retain more velocity without kicking the crap out of you if loaded correctly. Your problem is bullets, not muzzle speed or burning more powder.
