Doc,
Let me throw in a tip slightly off topic. Before you go, spend a little time shooting skeet. I have really found this excellent gun training in instances where you might jump your game in the thick stuff, taking a second shot on running game or need to finish off a charge. Your familiarity with mounting and shooting quickly will keep you calm and amazingly accurate at the ranges requires to shoot off hand at a moving target.
That said, the .375 is never a wrong choice. I you were to take 2, then a 30-06 with 165 grn TSX will shot the same trajectory as the .375 with 270's, and can deal with the smaller stuff. Still, there is no reason the .375 can't do it all. However, gun nuts are always looking for an excuse to shoot another.
