I’m going to answer your question in reverse order.
A purely American battery in 1924 would have to be:
Light- A Winchester Model 24 in .25-35 Winchester
Medium- A Griffin & Howe sporterized Springfield 1903 in .30-06 Springfield
Heavy- A Winchester 1895 in .405 Winchester
Your British medium bore could also be a .318 Westley Richards. This was an EXTREMELY popular medium bore during the 1920s. Post World War I, Cogswell & Harrison built these for several years on modified Pattern 14 Enfield actions.
Also, your German big bore magazine rifle could potentially be an August Schuler Model 34 in 11.2x72mm Schuler. Since it used a 400 grain bullet, it would be far more of a fair comparison against the .404 Jeffery.
The 10.75x68mm Mauser has only ONE thing common with the .404 Jeffery: The .423 caliber bullet diameter. It would be like comparing the .45-70 Government with the .458 Lott, simply because their bullet diameter is similar. The 10.75x68mm Mauser was always designed as an economic option for farmers and settlers in Germany’s African colonies, who weren’t interested in seriously hunting dangerous game. But just needed a handy general purpose bush rifle, which could afford some degree of fair protection against the odd livestock killing lion or rogue elephant or crop raiding hippopotamus.
My preferred British three rifle battery in 1924 would comprise:
Light- Holland & Holland Mauser 98 action magazine rifle in .240 Apex
Medium- Holland & Holland Mauser 98 action magazine rifle in .375 Holland & Holland Magnum
Heavy- George Gibbs Mauser 98 action magazine rifle in .505 Gibbs
My preferred German three rifle battery in 1924 would comprise:
Light- Original Mauser Oberndorf in 7x57mm Mauser
Medium- Original Mauser Oberndorf in 9.3x62mm Mauser
Heavy- August Schuler Model Jumbo in 12.7×70mm Schuler
Thanks very much for your reply/input!
A lever-action .405 combined with a British "light" rifle (in my case the .303, as I said) and a German 9.3x62 "medium" would certainly round out the trio, and for an American, having a Winchester seems an obvious choice. A pity it was mostly found in the '95 or in single/double-shot rifles, with the only bolt-action I know of for it being the Remington-Lee. I suppose there might have been some others out there but I suspect those are few and far between and likely didn't work as well as their owners would've liked. If we're restricting the "heavy" rifle to bolt-action magazine rifles, though, we'll turn to your other suggestions...
Good
God, the "Jumbo" action is an odd-looking thing! I went and had a look at some on google and they certainly fit in with my idea of blunt German practicality. Aesthetics (or at least sleekness) seem to have been sacrificed somewhat when that action was designed, but I wouldn't expect any less from them. I'm now given to understand that the 12.7mm Schueler was designed to (barely) fit into a standard M98 action, hence the rebated rim? I imagine you'd only be able to pack two or three rounds into the magazine for that. Was the 11.2mm Schueler designed for that too?
A .505 Gibbs would need a magnum-length action, right? So if one only had a standard M98 and didn't want to remove any metal or worry about modifying it, one would want to go with the Schueler round over the Gibbs or the .404 Jeff or .416 Rigby, presuming it fits?
But really, a heavy rifle like we're talking about is geared towards something like elephant and rhino and as extra-power on lions and tigers and bears; if none of those were on the plan or if your medium rifle was strong enough to take them cleanly, having a heavy rifle would be a bit superfluous, no?