An old friend of mine was an elk hunting guide in a Colorado Wilderness area.
His favorite elk rifle was a 308. When a client showed up with a 270,280,30-06,or equiv,he was happy. Past that,the bigger the gun,the more likely there would be problems. Especially if the gun was brand new.
Stan.check into what sort of hunt you are getting into. Some guides are into cross canyon shots. Way out yonder!.Big Magnum country/style. If thats what you want. Others will likely get you within a couple hundred yards...or less.
The cautions about 9000 ft altitude can be real. Talk with your outfitter.
If you are anticipating recoil,squinting,flinching,your gun is too big .Shot placement trumps all. I know a woman who kills elk just fine with a 243.Another uses a 257 Roberts. IMO,those cartridges are marginal for elk,but they can be used with the right shots. Brother and I cooked up a 165 gr ballistic tip load for a 14 year boy where recoil was a consideration. Two different years he took his elk,one shot kills,no problem. He only shot when he had a clear shot inside 300 yds. Hit a rib heart lung shot. Or pass up the shot.
IMO,you can't go wrong with 270 through 30-06,and a 308 is fine.No,I'm not saying you can't use a 7-08. IMO,as you go smaller,you have to get better. Closer,And more willing to pass up a shot.