The simple answer, I carry and use what I'm 100% sure works,and what I personally feel is the best choice, for me.
I would Not be overly concerned with the choice in rifles or caliber,
my late hunting partner used nothing but a 358 BLR loaded with 250 grain speer bullets
and my new hunting partner,is absolutely convinced that anything less than a 270 win loaded with 150 grain boat tail bullets will bounce off anything with fur.
the truth is that anything Ive seen used from a 257 roberts to a 458 win, works,
if you can place your shots accurately. (that does not mean a larger caliber won,t hit harder ,but dead, is dead and a 257 roberts 100 grain bullet placed in the heart/lungs is leathal)
your issue is NOT power its confidence in your rifle and Your ability to use it!
personally I've come to like the 340 WBY and 375 H&H, everything I've ever shot, with either rifle drops fairly close to the point of bullet impact,
but I can say the same for Rons 358 win and Bills 270 win
the main issue you face is finding a viable legal elk thats well inside your comfortable rifle range and placing your shot well,
thus good clear binoculars, the ability to read and accurately interpret topo maps, and good boots and the ability to stay warm & dry and in the field from before dawn to after dark,
to maximize,,your chances of being in the right place at the correct time is more critical.
Id bet theres thousands of Elk that are still wondering colorado each year simply because, many guys hunt hard the first two too three days, get frustrated & exhausted,
and spend the rest of the week or so sitting around camp or driving around looking for elk out of the trucks window rather than,
checking out the small side canyons, that might require a hour or so walking to gain access.
PERSISTENCE MATTERS, YOUR PHYSICAL CONDITION, and YOUR ABILITY TO SHOOT ACCURATELY MATTERS
BEING in the correct location at the correct time is not 100% due to luck! you can swing the odds heavily in your favor,
simply by constantly being in a reasonably likely location during the vast majority of the season rather than cooking hot dogs and drinking beer in camp.