What about the 9.3x62? Just stick to 232 and 250 gr bullets. Its close to the 375 yes, but running the lighter bullets its about perfect for the range and weight of game
Interestingly, there is no practical difference between 338 WM, 35W, and 9.3x62 when shooting 250 gr bullets.
232 gr Normas look very good at first blush, until you look at the very low BCs. They slow down in a hurry. If Swift made a 250 gr .366 Scirocco II, now that would be something worth looking at.