What if you pick your Elk bullet first. Just for sport take a SD around .28, and use Nosler partitions. 150g in .277, 160g in .284, 180g in .308, 225g in .338 diameter. How fast will a given cartridge actually shoot that bullet in the barrel length of a real rifle. Run the ballistics and look at the point blank ranges. Then look at how well you can shoot each rifle.
If you can put one of those bullets where they need to go, the Elk will be dead.
I look at the increased velocity of a magnum as a way to make it easier to hit the target by having a flatter trajectory and reducing wind drift. But if the recoil and blast adversely affect my shooting then any advantage in trajectory is lost by bad bullet placement.
I wish 280's came with 24" barrels.