I've killed one nice bull elk with my .280 Rem., using my handload with a 160 gr. Nosler Partition bullet. Perfect setup. Couldn't have been more than 160/175 yards, across a park, not spooked, broadside, and I was practically benchrested. One shot.
But since, my elk rifle is a Ruger .338WMag., and have killed four with that. I'd opt for a .338 WMag, if I were you. FWIW. J.B.