What's the terrain look like where you intend to hunt?
Where I hunt elk, you're going to be presented a shot at under 200 yards, or you're going to be presented a shot beyond 700 on the next ridge. Valleys are full of thick spruce, fir, and pine that you're not going to see anything through, let alone shoot through. Meadows seldom more than 200 yards wide. 200 yards is nothing for a .30-06, or the .270 for that matter.
If you hunt the sage country, you'll see 500-yard shots. A little long for the standards on elk, but certainly within the capability of the .300s. You don't need ANY .338 for that kind of distance.
Be ready though. Unless an elk goes down on the spot, he's likely to travel hundreds of yards or more before he even realizes his heart and lungs aren't working any longer. If you aren't precisely aware of where he was standing when you shot him, you may not pick up the blood trail at all - particularly when you're shooting from longer distances. "Was he next to this tree? Or, was it that one?"
I find a lot of dead elk in the woods come hunting season. I'm often left to wonder what the shot was and where, and why someone didn't find them afterward. It's sobering.