I would use a 7x57 and a .404 Jeffrey. And I would only use those two I think.
As a back up I would use a .318 WR.

(As for opinions of NZ hunters on game in the mountains - frankly the 7x57 or 7mm08 will do whatever you want it to do - and I have shot out to 400 metres and more with various calibers. Also, just to make a couple of points - One - you dont often need to shoot "long range' at all. Second - 400 metres ain't THAT far anyway...most everything will perform out to there. I have a friedn who loves the .243, long range shooting - and is a specialist Himmalayan tahr hunter.
So mountain use doesnt rule anything out nor require a specialist cartridge. Full stop.)