I agree with most everything that has been said, but I would like to point out three things.
First, you didn't say where you were going to be hunting and whether or not DG might be present. If there is no DG in the area, your .270 with well constructed bullets in the 140-150 grain class will do you fine, providing you shoot it well. However, if DG will be present in your hunting area, carry a .375 as a a minimum with a soft up and solids down in case you become involved in a "situation" with a buff, lion or elephant.
Second, one big advantage of a .30/06 is that you can shoot 180, 200 or 220 grain loads in it. Heavy for caliber bullets are do well in Africa, especially in bushveldt conditions.
Third, should your ammunition supply become lost in transit or should you run low on cartridges, it is much more likely that your PH will have .30/06 on hand than it is he will have .270.
I highly recommend taking two rifles. You can't go wrong with a well made controlled round feed rifle in .375 and a clone of it in .30/06 (or, I suppose, .270).