I have tagged several Wyoming elk in the last 20 years. Most were what I call eatin' size. By that I mean cows, spikes, and raghorns. The biggest was only 5X5. I have used '06, 280 Rem., 35 Whelen, 444 Marlin, and 6.5X55 SE. A variety of shot angles occurred but the bullet always found the heart/lung area. Some ran a little ways but never more than 100 yds. Some didn't appear hit even though they fell just out of sight. Others just stumbled around and fell pretty close.
I've learned a few very important lessons from elk that a truckload of whitetails, antelope, and mule deer never taught me. First, never shoot unless you are dead sure of making a good shot -- never take an iffy shot. Second, assume that your first shot was deadly and do not shoot again unless you are absolutely positive you are still shooting at the same animal. Third, follow up every shot by going on foot to the spot, searching for signs of a hit, and tracking until every possibility has been examined.
If you shoot an elk through the lungs it will die quickly even though it may cover some ground in the few seconds before dropping. The 6.5X55 with 140 gr. Nosler PT will do the job on any cow elk if the bullet gets to the heart/lungs. I cannot recommend neck or head shots for elk even though I have taken a few deer that way.
Work up the load, practice in pre-season and have faith in your skills and equipment. After all, elk are just big deer.
I am an old Missouri boy with ancestoral roots in NE Arkansas. The idea of elk roaming along the Buffalo River is just downright exciting. Good luck with your adventure.
2009 Spike Elk, Medicine Bow Nat'l. Forest near Albany, WY
Rem. 700 Classic 6.5X55 with Leupold FX 4X scope