A 9,3x62mm will save you a pound of carry weight and has a standard length action besides. It is a quite common calibre in Africa and is usually OK even where the .375 is the legal minimum for dangerous game. It was made for Africa!

For a bit more reach, the 8x68S is in the .338 Winchester Magnum class but is also lighter than a .375 H&H. One writer thought that the 8x68S was the best antelope cartridge ever invented. I wouldn't argue with him. The A-Square reloading manual states that in old German territories, such as Namibia, "it is the yard-stick,or meter-stick, by which all other cartridges are measured".

When I have been hunting sambar for 2 days, dawn to dusk, the 8x68S is much more pleasant to carry than the .375 H&H. It's a Mauser 66 which means that it has a telescoping action. Coupled with a barrel band, this means the muzzle sits quite a bit lower on the shoulder than a Mauser 98 style rifle with the same length barrel. That could be handy in some places too.