When I was looking into African plains game calibers, I was told "think elk", i.e. any cartridge that was adequate for elk hunting should do well for plains game.
When I went on my first safari last summer, I took a .338 Win. mag (didn't buy the rifle specifically for the hunt....had bought it a few years before I even thought about going to Africa) and my trusty .30-06. I ended up taking all but one of my critters with the '06 and a 200 grain Nosler partition handload.
Your 7mm should be more than adequate for the task at hand.
