I have shot several ( 4 to be exact ) deer with my .308 using 150 grain Nosler BT's out past 300 yards. Two were close to 400. I know this because they were all standing in the shooting lane of our club where we had metal gongs set up for practice. All were does - and weighed about 100 lbs. In each case I was sure of the range to the target and I was able to shoot off the bench. That is the only reason I took the shots. All were solid, double lung hits. All four deer were recovered.
Having said that, from what I learned from that experience I do not think I would try for elk much past 250 yards using my .308. There are better calibers much better suited for that task.