Africa Plains Game. Done it thrice; going back to Zimbabwe in September.
The idea of a backup rifle is a good one. Glass goes down; rifles get delayed by airlines. Were you without a rifle currently, I'd suggest a .338 WinMag. Only because it's the second most popular round (after .375H&H) among PH's there. It's as flat shooting as the 300 WinMag or 7mm Mag at ranges that are sporting and just seems to hit harder with a good 250 grainer. But you already have the 7mm Mag; unless you really want another rifle in the same class, the 300 WinMag 0r .338 WinMag make little sense.
BTW, my Eland in Tanzania was shot frontally with a 250 grain Sierra Game King. He ran 50 yards and lay down. Second shot was with a 250 grain Barnes X. On autopsy, the Sierra Game King (an excellent bullet) actually shattered on his breastbone and never penetrated the boiler room. The Barnes X did the trick. My point is that some of these animals will take a LOT of killing.
I agree with the suggestions that you go .375, .416 or .458. I will take it a step further and suggest that the "heavy" rifle be iron sighted. When you return for dangerous game (not "if" but "when"
) the iron sighted rifle will provide a heck of a lot better results if things start to hunt you back. A .416 Remington Magnum, for instance, will shoot every bit as flat as a 30-06....and there is no such thing as killing the smaller game "too dead"
Another alternative (my personal favorite for Cape Buff) is an iron sighted 45-70 or 50AK Lever Action. Few hunt those there and they always raise eyebrows when you demonstrate what they can do. Price is relatively inexpensive. Uses on the NA Continent extensive. Cool factor is off the scale, IMHO.
Enjoy the trip. Reports requested.