A gentleman I worked with for a few years (he's retired now) used a .243 Win to take 16 elk over the years. Several of which were very nice bulls. He used Sierra Game King 85 grain BTHP.

If I were to use a .243 I would load either 85 grain Barnes TSX, 100 grain Nosler partitions, 90 grain Nosler E-tip, or 80 grain Hornady GMX.