I've been lucky enough to kill five elk. Four were with my Ruger 77 in .338 Win. Mag., using my handload of 78 grs. Norma MRP (now, R22), behind a 225 gr. Hornady Interlock PSP. I had it Magna Ported, years ago. The rifle shoots 3/4" groups, wet or dry, hot or cold. Three were one shot kills, as the elk were standing still and I was well braced. None was more than 175/225 yards.
The fourth, about 325 yards, even though I was well braced, I made a bad shot (my fault, not the cartridge's) and my guide and I had to track the elk for five hours, Then one more shot, at about 50 yards did the trick.
The first elk I killed, in 1968, I used my Rem. 725 in .280 Rem., with a Nosler 160 gr. Partition bullet, behind 54 grs. IMR 4350. (Fred Huntington recommended this load to me, and it was/is extrememly accurate in my rifle.) Perhaps 60 yards, in the black timber. Broadside, one round, the elk staggered, then started to move so I shot him again and that was it.
Although I have other rifles, those are my two favorite calibers.
Having been fortunate enough to be in quite a few elk camps, in several states over many years, I've seen many calibers from .243 up to .375 H&H. Just guessing, more .30-06s than anything else, although the 7/30/338 Magnums are making a big dent.
HEY, SNAKELOVER, if you don't pull a Wyoming ticket, you might consider Idaho. We have a lot of elk here.
FWIW. J.B.