Went on a combo Muley/elk hunt a few years back with a Kinber 84 in 7-08. Being that both critters were on the menu, I settled on the 160 AB ahead of a case full of H414 (which really seemed to shine with heavier bullet weights). Consistent .75-.80 MOA for three shot groups.
Unfortunately, didn't get on an elk but whacked a mule deer buck at exactly 200 yds (lazed). It was a very steep quartering. Shot hit him behind the diaphragm on the right side. Bullet exited the lower left shoulder with about a quarter sized hole. He fell on the spot. Couldn't find bullet.
So, no elk experience with the 7-08 but i was (and still would be) totally comfortable with that load. But then again, like its parent, hard to go wrong with any decent bullet in the 7-08.
Good luck on your hunt.