ShootAllDay,
To me the rifle selection is perfect for the intended use and as for caliber I would ask you this question: Do you hand-load? If No, go with the 7mm-08, If Yes, go with the 280 AI. I am guessing that this will not be a high volume round count rifle due to the intended purpose of hunting. Either way both rounds are more than capable to 400 yards but the 280 AI will give better energy on target for heavier game such as Elk. In 2017 dropped a cow Elk at 422 yards with a 280 AI and 1 shot; so it will do it (handloads)
Cheers