Back on topic: A. Sharp,
Where in NC? I am in Georgia. Going on my first safari this summer!! I am taking my rifle for a few reasons, but mostly what jagaermeister said, knowing the gun AND THE SAFETY. Think how many deer or other animals you've missed or been too slow on because you didn't hit the safety or didn't realize you were shooting a different rifle/shotgun. Think dove field and a remington or a mossberg, one push-button cross-trigger, one tang mounted safety. When you are hunting dangerous game, do you really want to think about that.
To me, and this is my personal opinion, I'd try to get the same make and model that you are used to be it a remington 700, winchester 70, savage 110, ruger 77 etc... To me there is something about knowing the trigger, the safety, and the stroke of the bolt. All my serious rifles (4) are same make and almost identical triggers because I don't want to have to think about where the controls are.
Too, I have used my 375 for deer and hogs, big? Yes, fun? Most definately!! The slug is so big and fast that by time it thinks about expanding, it's through the animal.
The case is an investment to protect your investment. it seems like alot of money but over a 10 year period is nothing.
Lastly, I don't think the SAPS 500 and the customs forms are that hard, you have time, plan it, take your own rifle and cherish it forevr. Everytime you wipe it down, you'll be transformed to Africa and the lore, PLUS it's an excuse to go back, or plan your Alaska Moose/Bear hunt.
Just my opinion.