Elk can travel even with a well placed shot huh WTG.
If .308 is all you got, just try and stay within' a couple hundred yards or closer. Wapiti can be a nightmare to track. First some blood, then no blood, then no tracks. (Hope there's a little snow).
Bam, you've made cayote bait. That's my main reason to use bigger calibers, so you don't have to chase, and potentially lose, that trophy you went so far for and spent so much money on.