As far as the adequacy of a 300WinMag, given that a 30-06 will kill everything on the list, I'd say it is more than enough. More isn't necessarily better; especially for a youngster it could be worse. If you want to turn a happy trip into a terrible experience for him, give him a gun that beats the hell out of him. At that age, he will desperately want to "man up" and deal with it to impress Dad and show that he is no longer a little kid. But he sure won't enjoy it.
For plains game, if the 270 with a good bullet (Barnes, for example) doesn't kill it, I doubt a 338 or 375 will solve the problem. Yes, a 338 or 375 will allow him to make shots from worse angles, drop animals faster, and hit harder than a 270 will, but if he waits for a good broadside shot, and stalks to a reasonable distance, and shoots straight, a 270 will do the job. If it doesn't, it is more likely because it didn't hit the vital triangle than because of a ballistic failure. He's not likely to shoot the 375 better than the 270, so I really don't see the advantage for a 12 year old. If he were 70 and unlikely to ever return, I can see using a heavier rifle so that he can take marginal shots. At 12, he has time to be patient and if he can't get a decent shot, learning to let them walk is part of the process as well. Take the money you'd spend on hardware and get a copy of The Perfect Shot and have him read it cover to cover. He'll get more out of the trip and enjoy it more than learning to shoot a 375.
There seems to be this idea in America that animals in Africa require way more gun than they really do. I'm not sure if it has to do with poor bullets, poor shooting, poor understanding of shot placement, or poor authors trying to become rich authors by increasing the glamor of the subject material. Africa is wonderful enough without turing a Wildebeeste into a Panzer.