The only gun fit to carry when hunting game is the Savage model 99; having said that, you'd better get the .308 Winchester
. SORRY, I AM partial to the model 99's, and I do have one in a .308, but I choose to shoot within the means of both MY abilities and my rifle of choice.
As many have mentioned, nothing is more critical than shot placement to the vitals; the further your bullet gets from the heart, lungs, spine, brain, etc....the greater the chances of losing your Elk to the coyotes.
Another very critical point is to not push a rifle's capacity beyond it's limits; anything from a .270 130gr to a .30-06 165gr is more than adequate for Elk inside 300 yards providing you make a successful shot, but they simply lack the penetration at ranges much beyond that for an animal that could exceed 1000 pounds.
If you are certain that your conditions will require shots at 400+ yds, I would recommend nothing under a 7mm Rem Mag. In reality, the rifle I use for Elk in the "longer range" areas is a 300 Remington Ultra Mag in an A-bolt.
Another lesson that I learned while in the field is accurately estimating your shot distances. Four years ago, while hunting the North side of Mount Saint Helens for Roosevelt Elk with my WWII veteran hunting buddy Ken, we came upon a herd of roughly a dozen, including a few cow/calf pairs and two young bulls. The area was 3pt or better, so it was not our day to yield a kill, yet we did get something very valuable out of this venture. While on the hogback, looking across a ravine at the herd, I scoped each and every one of them and proudly stated to Ken that the herd was lucky that there was no legal bull, as I could easily hit each & every one of them, using the Alpine Fir as my rest. Two days earlier, I made a comment to him that I NEVER shoot beyond 300 yards simply because I am not that confident in my own abilities to risk a less-than-mortal wounding shot at a greater distance. After watching the herd lounge around for nearly an hour without a legal bull showing up, I pulled out a rangefinder that Ken's son-in-law loaned us, barely remembering that we had it in our midst. Much to my shock, the Elk were between 385 and 405 yards away! My estimation BEFORE pulling out the "proofreader" was 275 yards, and I actually thought that I was a pretty good judge of distance!! Talk about a dose of humble pie! Regardless, the humility of being off by more than 100 yards was easy enough to swallow, but it did make me realize that particular conditions in the elements and terrain can cause errors in judgement, hence, increasing the possiblity of an errant shot.
Bottom line, if you say 400 yds, unless you have a rangefinder, you may just as well be shooting 500, 550, etc. This is why the larger, longer range cartridges would be my suggestion. As I have said along with many others, shoot within the means of your rifle and your own abilities and you'll yield good results. Now get yourself that Savage 99 in a .308 and save me an elk Tenderloin
! Happy Hunting.