375 HH is world known as universal caliber from steenbok, to elephant.
Also, in most of the African countries it is legal minimum for DG.
338, is below legal minimum in some countries for DG.
416 is "overkill" for plains game, and 458 also.
So, 375 is for all, and almost no other is equal to it.
you can consider 375 Ruger, or 376 steyr, if that rifle will be easier to find.
2 Gun and 3 gun batteries:
if you want to do multiple safaris in the future, 2 gun battery may be considered.
From your choice of calibers: then 338 plus 416, or 338 plus 458 would be a good pair,.
3 gun battery
Bird hunting becomes very poplar in Africa, you may add a 12 GA, with above two gun battery, and you can hunt anything. Note, many rain forest duikers are as well hunted with shotgun, if you ever plan to hunt in the rain forest.
Neverthess, one gun rifle for all 4 legged game, is 375.
Me?
After 3 PG safaris, and one in future:
I stick to 375 for all, and dont plan any other mutliple rifles batteries.