Brian (OP):
Lots of opinions and I'll add mine, but want to ask you one question. Do you reload or plan to reload as this opens an entirely different world. But, based solely on your original premise of US deer and African PG and presuming you will get into reloading if not already doing so I would suggest the 375 H&H or 375 Ruger. Mostly because you can always load down but you can't always load up.
Just did a quick review of the Hodgdon Reloading Data web site for current data, the 7x57 max is a 170gr bullet at around 2300fps and the lightest bullet listed for the 375 H&H is a 200gr bullet at around 3000fps and the heaviest is a 300gr at 2650fps. Yes, there are some heavier weight bullets available for both, but I just wanted to use publicly published reference data.
Historically, the 7x57 has taken every animal in Africa including the "Big 5". However, under today's caliber, muzzle energy minimums/restrictions (including PG) in some countries and provinces in RSA, it may not be legal for all (biggest) of the PG species while the 375 H&H or Ruger, with appropriate loads, is legal for all PG and DG.
Then too, depending on where you hunt in the US the H&H with those 200gr maxed out is pretty damn flat shooting for use out west for pronghorn etc. Plus, if there is also the possibility of larger bodied game. elk, moose or bears in the US the H&H still would get the job done very well. If there is a possibility of hunting in the US for anything more than whitetail somewhere down the road a 375 might be the way to go.
Personally, eight trips to Namibia with the ninth planned for next year, all PG so far, and hoping to time things right if a PAC ele comes up - keep a bag packed for a short notice trip if my PH friend gets the green-light on one. We've used, 308 Win, 45-70/450 Marlin in lever and custom bolts in both, 375 H&H and 375 Ruger and once with 458 Win Mag. We (wife and I) have migrated to the 375 Ruger in the Alaskan configuration for the main reason outlined above i.e. moderate velocity 250-270gr loads for her keep the recoil level where she can shoot it all day at the range and I load some 235 TSX at 3000fps for long range baboons in the mountains and 270gr for everything else and a few max load 300gr solids for both of us just in case we get into trouble with ele in the area we hunt.
Biggest point to think about is to make 100% sure the caliber you are using is capable of meeting the muzzle energy minimums for the species you are hunting in the country or province you plan to hunt and to remember that calibers that might be legal for a "local" to use may not be legal for a "foreigner" to use. The last thing you would want to do is get caught in a Lacey Act violation as remote as that possibility might be.
