When I first moved to the West I wanted to go Elk hunting and started to read everything I could about the rifles and ammo.
Everyone said 300 Win mag as a base. When I started to read about 300 Win I found it was made in the late 50's shot the same bullets as my 308, but 200 to 300 FPS faster. All it did was change the trajectory and extend the range. When I read that they did not like 30-30 but said 44 Mag was a great elk pistol round, I smelled something fishey. The 30-30 has much more horse power than the 44 mag. The handgun barely breaks 1,000 foot pound and the 30-30 has more than twice that.
Yardage being the big factor. Hunting with a handgun you will be well with in 50 yardds much like Archery.
My next question was before the elk slaying 300 Win came out what did people use for elk? and found, 30-30, 32 Win Special, 30-06, 30-40Krag, 45-70 and even pistol rounds like 44-40 and 45 Colt were used. .50 Black powder front stuffers are used and they have about the power of a 44 Mag / 45-70 carbine depending on the weight and shape of the projectile.
The question is not what will kill an Elk but how far away you need to be with that (rifle, shotgun, handgun, or Bow) you are from the animal.
I think you would be better armed with a 308 you use on a regular basis than a new super belted mag you do not shoot well. My guide was not too happy to see me with a new looking Win Model 70 in 338 Win Mag. Till he saw some knicks and scratches in the wood, metal and stock and asked what I had hunted with it before this trip.
What I did was go to sportmans warehouse and buy the elk targets. It shows an X ray of the animal where the leg is as well as where the heart and lungs are. (they also have them for coyote, deer, pigs and antelope
Buy them and practice shooting at the targets at different ranges before you go. Either go with a heavy for caliber round or one of the lighter premium rounds like the Barns X that is light but still the same size as the heaver rounds. The copper is lighter than the lead and you need more of it. If you are willing to hold your shot and wait till you get with in 100 yards (most Elk are shot with in 100 yards) then bring one of your larger bores and just wait and sneak in or wait till they walk up to you.
Good luck on your tip.