I've never hunted elk. I've been reading about elk-shooting for many decades. So, take this for what it might be worth.
A primary requirement, overall, is a cartridge and bullet combination which will reliably give deep penetration on a quartering-angle shot. Sure, lots of lighter-weight combos will break a neck, or destroy the heart/lungs on a broadside shot. But those are ideal situations, and unless you're highly skilled at stalking, or lucky on how an elk is standing, you can't rely on "ideal".
As a novice elk hunter, I'd rather be a bit over-gunned than under-gunned. Looking at what I now own, however, I'd stay with my '06, since I've been using that rifle for over thirty years and am "married up" with it. I'd load some good 180-grain bullets and be fairly confident about my chances.
Regardless of all that, though, we gotta remember that a lot of elk have fallen to .270s and .308s...
Art