I'll add another thought.
While I don't think many of us would question the ability of a 6mm Rem/.243 Win to kill an elk. There is the question of how fast would it kill it and how far it might go before it died.
I'm familiar with incidents of people shooting elk in crowded hunting areas and tracking it down, only to find other hunters claiming its their elk. Perhaps looking into neck shots with the 6mm might be worthwhile?
I've only ever killed two elk and they were with shoulder shots using a .338 Winchester Magnum. So I can't be much help on smaller caliber advice. I/m sure one of our more experienced elk hunters will come along and offer more/better advice.
"No free man shall ever be debarred the use of arms."- Thomas Jefferson