Any particular reason you want to hunt on private property? Head up to the NE part of Medicine Bow. The area up there is over objective. I'll be up there later this month on a scouting trip, then 3 weeks hunting from Sept-Oct. If you're not interested in getting in a mile or two(which is about all you can anyway up there) there are plenty of old logging roads you can stroll up/down.
Thanks for your advice Brad. I've never hunted Elk or in Medicine Bow before. I'll be there for 2 weeks hunting Area 42 antelope and decided to try my luck on an elk tag close by. .