The Two Dot does allow access for hunting cows at least. A friend of mine from Powell just gave me that info, because I was trying to get a cow permit there (should have applied first round). He said that sign-up starts September 1 and is $40.
It's always been open to Hunt, fella from Switzerland owned it for years now a company from India doors, at least what I read a year ago or so, was in the paper.
The game manager was a retired warden from here, don't know if he is still there or not, made sure hints were pretty darn good
Pitchfork ranch is another that head fee access, never heard anything bad about them either, and hunt oil company, dba hoodoo ranch, has 7 or 8 properties that they used to allow fee access to, not sure if they still do but probably do.
Wgfd is always a pretty good resource though I've not found the cody office to be as helpful as other offices
BLM is hands down the most helpful all the way around with Shoshone national forest a close second, there are certain ranches the elk are stacked up on, but hunting a ranch DIY walk in isn't probably any better than on public land.
For a week sometimes I can't get to my mailbox without pushing 50 elk out of the way, then for no apparent reason I won't have one around for miles for 2 weeks, then POF! They're back crappin on the deck.