I've done the plains game thing with a .375 and was not wanting. I loaded 260 Nosler Partitions to 2800 fps (could likely get a bit more). Sighted 2" high at 100 its good for about 250 or so without holdover. I put a Leupold VX3 4.5-14 with the Boone and Crockett reticle sighted for the various holding points in the event a longer shot was required, and it came in handy on a 300 yd sable that wouldn't let us get any closer after several attempts. Yet there was no problem snap-shooting a kudu at 25 paces.
When I went back I had upgraded the scope to the VX6 2-12 with that custom CDS dial, a wonderful thing for the .375 and my PH loved it. In fact he instructed me to never change it, stated he believed that many clients under scope their .375's then try to take 250 yard springbok shots at 4X and muff them.
On that trip I also took a .280 Ackley with 160 Accubonds @ 2950 fps clocked (basically a 7 Mag) wearing the aforementioned VX3. PH didn't want me to use it on anything larger than a waterbuck. It worked really well on the waterbuck, but it came into its own on a herd of about 100 blesbok, probably 5+ of them SCI Gold, that wouldn't let us get anywhere near them. The .280 AI solved the problem when we finally got a shot at 336 laser-ranged yards, holding just a tad high on the second wire. May or may not have taken that shot with a 300 gr Barnes TSX, but would likely not have that Gold Medal Ram if I hadn't.
That's an outstanding battery for RSA, a 7mm/.300 and a .375. You didn't mention if you've been to Africa before, but I have to say there's nothing wrong with a .25-06 or .270 and a .375 either, use the smaller, flat-shooter up to blesbok and such, the .375 from there. To my thinking the .338 would be good for a one-rifle safari on plains game, but too close to the .375 if taking both. Not much difference in felt recoil or trajectory either. My PH carries a .338 all-around and a .416 for dangerous-game back-up so I don't need to.
The only reason to go over the 7mm to the .300 would be perhaps wildebeest-sable-eland, 7mm is perfect for springbok, blesbok, impala and similar sized animals, but if you have the 375 along you'll be well-prepared for it all with just about any flat-shooting cartridge from the .25-06/.270 on up. My pick is a 7mm with 160's.