If you really want to shoot that distance I think to only two options are 340 WBY and 338RUM, both shoot flatter than either a 338 Win Mag or 375H&H.As much as I like a 338Win Mag, the range is very similar to a 30-06. IN the end, I don't think either is the best choice for what you describe. I would get a 300 RUM as a second rifle, and learn to reload ammo. Go with a high quality 4x12 scope and practice, practice, practice.

IMO 375H&H is not a long range weapon.

Good Luck