Just offering some thoughts ...
Best "All-Around" Plains Game Caliber.
One way to look at this question is from a historical perspective, which asks what cartridges and loads were deemed the most successful on African PG in the pre-WW2 period (roughly 1918-1940). Then look for what modern analogues exist.
If you read the classic accounts of African hunting (e.g., "Pondoro" Taylor and others), the most popular cartridges for PG early on were the .318 Westly-Richards and Rigby's .350 Magnum. Holland's .375 came later as its answer to the Rigby .350.
The .318WR sent a 250grn bullet of .330" diameter @ or near 2400fps. It was accurate and felt-recoil was deemed mild even in light-weight rifles.
The .350 Rigby Magnum launched a true .358" dia bullet of 225grns at a
claimed m.v. of 2600fps although that was never matched in the field. Real-world velocity of the 225grn load was more in the low-to-mid 2500fps range - variously stated as 2520-2550fps. A 250grn load was developed later, sending a SP bullet in a similar m.v. range circa 2550fps.
The Rigby .350, in particular, was favored for PG by famous old-school African hunters such as Denys Finch Hatton, Peter Pearson, Baron Bror Von Blixen, and of course, Taylor.
The .375H&H really needs no detailed review of suitable loads or of its historical field performance on African PG. If that's the rifle you're taking, just pick a tried-n-true load for the species you intend to hunt, dial it in, and have at it.
For a modern American analogue cartridge to the .318WR, the .338WM obviously comes to mind. Solid loads exist using 225grn and 250grn premium bullets and would basically duplicate the .318WR's performance on non-dangerous PG.
Two older American analogues exist for the .350 Rigby: the .350 Remington Magnum (the world's first Short Magnum) and the .35 Whelen, also known as the "Poor Man's Magnum." Either would be highly effective on PG; the real difference is in the size and weight of the package.
.35W rifles are built on long actions (.30-06 length), whereas the first Remington .350 RM rifles were built on short-action carbines weight 6lbs with 18.5" barrels (the model 600s). Afterwards, using the same short-action, Remington built 7lb, 20" rifles (the model 660s). Ruger once chambered the .350RM in its long action M77 rifle.
More recently, Lipsey's marketed a Ruger African rifle chambered in .35 Whelen.
Regardless of the package, either of these .35-cal cartridges has proven capable of taking down The Big Stuff, ranging from feisty moose to the huge AK bruins. So there's no doubt either could match the record of Rigby's 350 on African PG.
The .350RM can push 250grn bullets into the 2450fps range generally and, with some powders, at circa 2500fps, and that's out of a 2.800" short-action and 20" tube. In the
long-action Ruger 350RM with 22" barrel, where you can long-load bullets, you can get higher velocities. (See Ken Water's chapter on the .350 Rem Mag in his tome,
Pet Loads).
The Whelen's real advantage, again due to its COAL and a long-action rifle, is the ability to shoot the heavier 300grn/310grn thumpers if you need to go that heavy.
But then a typical wood-stocked .35W rifle, with scope, mounts, and sling, is running north of
9lbs unloaded. The unloaded weight of my 20" model 660 - decked out with scope, sling, stockpack - is just touching
7.9lbs. (Obligatory pic attached).
So, loaded with premium 250grn bullets, in an easily carried package, my M600 would be my choice for hunting African PG. (I'm sure my custom .375 H&H BRNO 602 would be jealous

) .
M600 in .350 Rem Mag