There is some public land on the unit, but you will need to put in some time. I am related to the Kearls through marriage and can tell you Clint Kearl is a real special person. He runs his cows on the national forest just so he can have good habitat for the elk to hang out on. He is one that gives the cow ranchers a bad name by abusing the public land and his grazing permits. When I was much younger I took a B&C moose that had wandered off of the Kearl estates onto public land....ha, ha, silly Clint. I haven't been up there in years, but used to hunt quite a bit in that area. The prior drought really pushed the elk off a lot of that unit. We used to see a lot of animals in the Quaken Aspen Springs area, but after several years of over grazing, nothing was left. That's why I don't hunt there any more.
If you want to try getting on private property, I'd talk to the Wamsley's over in Round Valley. You might have to pay to trespass, but they have some decent property, and are much more polite than Clint.