We just got back from Africa. One of the rifles that we took was a semi custom 257 bee. This rifle was set up with our 116g Sledge Hammer. This rifle took 7 animals from porcupine to trophy eland. Most of the animals that were taken with the 25cal would have normally been considered too much animal for the chosen cartridge, according to the professional hunters. After seeing bullets performance they had no problem letting the little 257 take any plains game available. All animals taken were one shot except the eland. The eland, for those who do not know, is an 1800 lb animal. The 1st shot on it was frontal. The bullet was recovered in the small intestines. The second shot was not needed but taken because the animal was still standing. This shot went through the massive shoulder bone and stopped in the brisket. Both bullets identical after recovery. 87% retenetion. Along with the eland the list of animals includes trophy common blesbuck, zebra, trophy impala, trophy white blesbuck, warthog. All one shot kills with little or no travel after the shot.
Long way of saying your 257 will be fine for elk with the right bullet. Remember most bullets are too frangible for the speed or too long for the 10" twist that the 257 has.
Steve