I have had good hunts thru the years at the Pitchfork Hunter Management Area just east of Pickett Creek. There is a large gently sloping plain between Carter Mt and the Greybull River that has plenty of speedgoats. I like it because it is at a higher elevation than a lot of Unit 82, a bit cooler and maybe more moisture too.
You have to go to the WGF website and find the HMA info to get a free permit, map, and area ranch specific rules. But not really too many hoops to jump to gain access to a good piece of property.
Another area you can add is the Greybull HMA, also lots of public land in the YU Bench region, a bit drier country but holds a fair # of goats.
One more thing, if you are looking for a real good trophy, you'll need to cover a lot of country and look over a bunch of animals, and still may not find one.
If looking for just a good representative sized buck, you will have a great time.