If this excursion is primarily for hunting game, my two choices would be my 7x57 Rolling Block and my friend's Marlin 45/70 SBL & some Barnes (or Buffalo Bore or Garrett) ammo for the really BIG STUFF!
Nobody else would likely have a Rolling Block on this safari (although it has been reported the Mauser was the choice of a famous African BIG 5 hunter as well as Mrs. Thompson) and it truly would be a once-in-a-lifetime opportunity...
If for purposes OTHER THAN primarily hunting I might have to go with Mr. Thompson's fave, 270 Winchester in my Ruger M77 Ultralight and one of my MSRs with 5.56 & 300 Blackout uppers to handle any "restless natives" that we might encounter on the way?
Cheers!