"What do you guys think that is the ideal battery if one is pursuing lion, leopard, 3 buffalo and tons of plains game on a 28 day hunt?"
Several important considerations not included in this hypothetical scenario, mostly country, area and terrain. So, given that this would be for the country of "Anyplace". I'll offer up my limited opine.
For the game specifically mentioned wherein I would be the "client" and not the PH, It would just be two calibers/cartridges: 30-06 and 458WM.
My personal rational would be having to consider the 5kilo max airline weight limit on ammo. Given the, "and tons of plains game" being a pretty open limit, there could be a reasonable possibility I might have to purchase/acquire a little additional ammo at some point. Both calibers/cartridges are pretty easy to come by in most of Africa. May not be the projectile of choice and may have to play with zero a little but at least I can still go "bang" and not have to use my rifle as a fancy club.
Within that .30 and .458 caliber limit, the projectiles the 30-06 would be 180gr TSX and a few 210gr Cutting Edge Bullets (CEB) brass solids. For the .458, it would be CEB 420gr Safari Raptor and 450gr safari solids.
Rational for the above projectiles:
I picked the 180gr TSX over the TTSX is because the TTSX open/mushroom quicker than the regular TSX. If the PG is say, "the Tiny 10" the TSX is less likely to damage hides for trophy mounts and less bloodshot meat for the potjie pot. On the bigger game all the way up to eland they will penetrate to and through the vitals plus some. The reason for a few of the CEB 210gr solid that would and in fact are in my pocket if I'm carrying a 30-06 or even a 308W where jumbo might be encountered is from the testing I've seen in wet newspaper from 50m and the few I've actually tried on a couple of zebra end to end, I am confident they will pretty easily get to the brainbox on an elephant in a pinch.
The reason for the CEB .458 Raptor/Solid is the Raptor is designed to that instead of just mushrooming, they are machined to have "petals" break off after impact which act like a mini hand-grenade going off inside the rib cage while the remaining "shank" becomes a flat nose solid and drives though the vitals and usually exits. They noses are shaped and the weights are close enough that you can pretty much use them interchangeably without having to re-zero. They do make a .470gr Raptor and 500gr solid, but since the country is "Anywhere" Africa, the slightly lighter weights might shoot a little faster/flatter and not give up too much penetration.
Granted, non of these would be likely available off the shelf or from under a bush outback but, by the time I shot up 5k of ammo, I'd likely be near the end of the 28-days.
Like many on here, I'm a big fan of the .375's. Had an H&H and got rid of it when I got the 375 Rugers. I didn't choose it in this case mostly because of the potential to being a bit more difficult to find in some African countries. If the ammo was unlimited it would be a 375 Ruger with 270gr TSX and 275gr CEB Raptors and 300gr CEB Safari Solids. The other consideration is the usual 100rd per caliber importable quantity of ammo. Two rifles means 100rd for each, subject to the 5k airline weight limit.