The allure of big wilderness sounds grand to those without experience. I take a different approach, look for what elk need, what elk want and what I can access AND retrieve a bull from.
A couple of miles and a couple thousand feet sounds pretty easy on the internet....add in the drag of vegetation on your boots, altitude, lack of sleep and suddenly it's a lot to ask.
I suggest finding small areas that offer everything and are not a destination for horses.
Horses need places to park the rigs, feed, a reasonable trail....etc.
The quickest and easiest to make work for you is the parking. Launch at an area that lacks parking. If it's 10 miles to the trailhead, and not many horsemen are going to bushwack, you just bought a big cushion.
Think about the elk needs. They need to not be seen by every car that passes, but they tolerate hearing them without issue. They must have food and water. They must have a bedding area. They seem (rocky's ) to like .5-2 miles between food and bedding.
Look for places that can work thermals and prevailing winds to the animals favor that fit the above and you're on your way.