What would you suggest? I have also found dead not recovered elk, but I can't say any of them were because a .308 didn't do its job! Even with old green box, ammo. No way of telling with what caliber they were shot. Could have been a .22 or a 460 weatherboom. Shot placement.
I have shot and seen plenty of elk killed with plain ol' c&c bullets--which is why I prefer premiums. Cuts way down on the elk drama. My family has owned land in the high country of west-central Colorado for several generations. I've been finding dead, unrecovered elk since I can remember. In some cases the elk were fresh enough to find bullet holes, and most had bullet holes in the front half. A one lunged elk can cover a lot of ground in a short time. In dry conditions and thick timber, it can be very difficult to find an elk that travels 500+ yards before it dies.
Partition, TTSX, or E-Tip are my first choice. One can spend a lot more money on the boutique premium bullets, their terminal performance isn't any better, but a particular rifle may prefer them.
It's not the cartridge, it's the bullet that counts. I have a pair of 243's that have now accounted for 15 elk with 100g NPt's--mostly in the hands of youngsters. Hunters being hunters, we still want to focus on the cartridge, when we should be thinking of the bullet.
