Personally I subscribe to the old adage that shooting elk is the easy part, and finding them is the hard part. Depending on where you hunt of course, if you have access to quality private land then the equation changes.
Assuming that finding elk is the hard part, you'll be doing a lot of walking, maybe in steep terrain, maybe not. So I tend to go with the rifle I want to carry in the mountains. I have a few purpose built "long range" rifles and they tend to be on the heavy side so I don't normally find myself reaching for them when it's time to head up the mountain. I can't really get behind the idea of a lightweight .338 LM or .340 Weatherby, setting aside the fact that they're not really needed. So to me, out of the cartridges on your list I'd go with the .280.
If you can't kill an elk with a .280, it's not the cartridge.
