Eileen and I have used the .30-06 on a wide variety of plains game up to 800 pounds, including all those you list, using controlled expansion bullets of 165 and 180 grains. They worked fine, at ranges out to 350 yards--and that shot was an instant kill of a kudu bull, with a 180 Partition.
But Eileen has also used the .308 Winchester with 150-grain Nosler E-Tips on the same variety of game with zero problems at the same ranges, and I've used the 7x57 with various bullets in the 160-grain range with zero problems.
Have also been beside various friends who had the similar results with the .270 Winchester, .270 WSM, 7mm-08, 7mm Remington Magnum, etc. etc.
The "extra toughness" of African plains game is one of the enduring myths among American hunters. I partially blame Elmer Keith, who used a .333 OKH as his "light" rifle on his first safari in 1958, with 300-grain Kynoch soft-points that blew up so badly one didn't exit a Thompson's gazelle, about the size of a big coyote. So he switched to the Kynoch 300-grain roundnose solids he also brought, which didn't blow up--but also didn't kill very quickly. One zebra went several hundred yards before it went down. From this "evidence" Keith concluded that all African big game is "as tough as an old gum boot," but he would have done fine with a .30-06 and 180 Partitions--which had already been available for a decade.
We have used the 7x57, 8x57, 358 Win and 9.3x62 as well on similar critters there. All worked fine with about zero difference in effectiveness, not surprisingly.
