Ditto on the 30-06 if you just want an elk. My family and I have killed a truck load of elk with 06, both Rocky Mtn. and Roosevelts, at long and close ranges. You already have it, likely have it sighted in with a hunting load, and are familiar with it. Depends of course on your personal goal: whether to get an elk or to hunt elk with a particular rifle/cartridge. Either goal is legit, but work best if consciously and deliberately chosen by you.

Having said that, my son, who went to a Tikka Lite stainless synthetic in .338 about ten years ago, has toyed with the idea of getting an AR in .338 Federal. He mostly hunts Roosevelt elk in wet jungles. I don't think he is very serious about the AR in .338 Federal but he has killed most of his elk at ranges under 75 yards, including two B&C bulls. I'm thinking he killed one Roosevelt at maybe 275 across a canyon, but last year's in brush at 40 yards was more typical.