Matching cartridge to barrel length is the key. I've had short barreled .350 Rem Mag, 376 Steyr and even a 18.5" barreled 7mm-08 that where real flame throwers.
Cartridge efficiency is key to short barrels. I generally do not have any shoots past 350 yards, so a "big gun" is not needed.
The original poster needs for Elk might rule out any cartridge suitable for super short barrels (16"-18").
If going with a .308 based cartridge I would recommend 19" plus.
Going lower than 18.5" it would be something in the smaller class.
6.8 SPC is pleasant out of super short 16.5" barrels.