With the 30-06 and the 375 in your hunting line-up, you'll never go wrong. You'd be hard pressed to find a more useful and all around great "meat on the table" cartridge than the 30-06. Add in the 375 and you've got a great battery of rifles. The two together should allow you to take all game in N. America and most (no, not all) game in the world.

I'd say you've got what you need - now go shoot them!

-Vlad