Drawing from what I have, and have seen perform, it would be one of two rifles depending on conditions. IE, are we talking demanding, physical, mountain hunting or does this lottery include getting ATV'd to within a mile of where I'm hunting <grin>.
If it's a "normal" elk hunt, in other words very physical, I'd be carrying my M700 XCR in .338 WM, a 3-9 Conquest up top, loaded with 225-gn Accubonds at 2860 fps. This is an extremely accurate rifle and I've practiced extensively with it to 625 yards. I've yet to hear an argument against .338 WM for elk other than recoil. For whatever reasons that's a non-issue for ME with this rifle so there you go.
If, however, it wasn't a physically demanding hunt, I'd carry my M700 Sendero II SF, with a Zeiss 6.5-20x50mm on top, Jewell trigger set to 6 ounces, wingin' 200-gn Accubonds at that same 2860 fps. This is an extremely accurate rifle also and would give me a bit more reach.
It's very unlikely I will be hunting such a tag anytime soon.
