An eland is a big animal, but it doesn't have giraffe or hippo skin. I've taken eland with both a .300 Win Mag as well as a .375 H&H. I can't say that I've seen enough of a difference between the two to suggest that a .300 might be a bit light. So I'd be just as comfortable taking the shot with the .300 as with the .375.
As for the .308, it's a bit lighter still than the .300, but I don't think I'd worry about it. If you put a .308 bullet and a .375 bullet in the same place on an eland, it's just as dead. On the other hand, if you don't put either one in the right place, I'm not sure you have a better chance of recovery with the .375 - this is an animal that can run all day when wounded.
Having said that, I'm always a fan of using whatever you're most comfortable with so long as it's legal and ethical. In my view, the .308 meets both those tests, so if you don't want the kick of the .338 or bigger, or even the .300, the .308 is a good bet. On the other hand, if you're looking for an opportunity to use the 9.3x62 or the .375 (and I often am looking for an opportunity to use something bigger from the cabinet), then you should do that!