MinnFinn

With a heavy boned and tough hided animal like an Elk, especially as you likely end up at further distances in the West, I would not hunt with such a light caliber rifle as 6mm or .243. It may be that it "can" take down such an animal, that doesn't mean it's the ideal rifle or that you "should" use it.
I'd stick to a heavier caliber (.30 or .338). I know that a number of people hunt with .270 or similar successfully. I favorite is .300 WM. Zeroed at 200 yards with a bullet designed for deep penatration, it'll go through an Elk's shoulder, lungs and take it down out to over 300 yards, as long as you can put it on target. I don't think that your lightweight bullet will do that without the greater likelihood of wounding and loosing Elk at less than ideal shooting conditions.

Dirt2

Back in '78, we had just moved to Montana. My dad went out on our first hunt and killed a 353 net 6x6 bull - with one shot through the lungs from a 6 mm. The round will work.

You do have to make significant compromises on shot selection - avoid paunch and shoulder bones and long range - but in a pinch the round will kill an elk. (By the way, these are the same compromises that bowhunters make, so I laugh when I hear it can't be done.) The bullet will almost certainly not pass through an elk, so your blood trails could be sketchy.

That said, more gun is probably preferable, unless you have a truly pressing reason for going with that caliber.