My personal choices are the 300 Win. Mag. and the 338 Win. Mag. The 375 H&H is completely unnecessary, and a burden to carry.

If you don't want 300 and 338 type recoil, you can go with the 30-06 any do very well.

I've used the 300 Win. Mag. as my only plainsgame rifle on all of my safaris except for one, when I went with the 375 H&H, and I've used it to take all of the species that are on your list, plus many more. The 300 Win. Mag. has never, ever let me down, and it's dropped stuff just as hard and fast as the 375 has, plus it's lighter to carry, kicks less, and shoots flatter as well.

AD