You will be at an impact velocity in the 1200 to 1275 range with the Berger at 4000' asl. So I say which ever one you can drive through the heart.
Expansion will be hard to get with any of them.
I would not count on that BC of the Nossler, I feel it is less, so I will count on less impact velocity for it from my experience.
I have 3 reports from friends I trust on game killed at 1600, 1775, and 1697 this past season. These are the only info I can trust. 3 different bullets, the Berger OTM, Berger Elite Hunter and The SMK all 300 gr. The EH was from a LAI and was at 1600 yards but it did expand. The others were not in the shoulder either and didn't expand.
There is a reason I went to a chambering that gained me 400 fps. And if I engage an animal at a mile I will be sending a Berger. From what I have seen the EH with a MV of close to 3K has done the best at expansion so far. So with my MV of 3200 it is doable when all the stars align.
So, 2800 MV, put it in the shoulder, heart or real that distance in and make sure you have a clear view of where the elk could run to and be ready with a good spotter for a follow up if needed.
Good luck trying to have this discussion. There are only a hand full of people that truly know what really happens at these distances. But opinions will rage on.
Jeff