I think I would go old school and do a .318 WR, or a 333 Jeffrey but with .338 bore or a 350 Nitro Express. Brass is available though expensive but it is a one time expense.
Anything from 8mm to .40 on the 06 case would be a good one. Probably go AI on the 400 Whelen just to get more shoulder. But I think the 9.3 or 35 Whelen would be the most practical. I would also go British express rifle for the stock like a Gibbs, H&H or Jeffrey with short stalking rifle fore end and Whelen or pancake cheek piece and then I would agonize on whether to Schnabel or not to Schnabel the fore end. The .375 Whelen is also a versatile choice.

"When you disarm the people, you commence to offend them and show that you distrust them either through cowardice or lack of confidence, and both of these opinions generate hatred." Niccolo Machiavelli