Guns for Africa?

[Mr. 16 gauge]

O.K., this post is kind of an addendum to the earlier post I had made entitled "Guns for Africa". My friend and I have been talking and it looks like we will attempt to hunt 'the dark continent' in a couple of years.
Having said that, I've been checking some websites. We are planning on doing plains game only (for our first hunt...who knows, we might go back!) and the species list contains the following: Kudu, Gemsbok (Oryx), wildebeest, Red Harebeest, Zebra, springbok, and steenbok. I realize that the smaller antelope will fold readily to my trusty '06, but I am wondering if the bigger antelope (kudu, oryx, ect.) ...........would my .30-06 with 200 grain Nosler partitions be up to the job? I really don't want to have to buy a bigger rifle; I am a bit recoil sensetive. The above mentioned load I have worked up will shoot a 1/2" group at 100 yards from a bench.
Some of the stuff I've read on other sites makes it seem that the .338 is minimum. Some of the websites say "30 cal minimum", but I don't know if they are talking 30 caliber magnums, or something along the lines of the .308/30-06.
There is also a lot of crap out there.....a lot of the '.375 H&H minimum" opinions are from people who have never been to Africa, let alone hunted there.
I don't want to go and look foolish....or worse yet, loose a wounded animal. I guess I"m also intimidated by the potential recoil of the bigger guns....does a .338 kick much more than my slug guns?
At any rate, thanks for taking a look at this post and expressing an opinion.