Your .30-06 is a little on the light side for Eland but with a good bullet and patience to make a good shot, it will work. And thus, it will work on everything else on down.
That said, a .375 or the 9.3 is all that much more of a good thing. A .375 shooting 250gr bullets will give you roughly the same ballistics as the -06 shooting 180gr bullets.
If you opt for one of the larger calibers I'd go with the .375 as you'll meet the minimum caliber required for DG whereas that can't be said for the 9.3 in some places.