Doe and buck tag permission on private is night and day, especially if you are flexible and can go late season or whenever they aren't busy or booked. The best odds would be irrigated farmland with tons of goats that eat their paycheck, if you have several doe tags you will have a much different conversation than one buck tag from a guy very particular about what you want to shoot. If you have a big checkbook, you will always have willing landowners, but doe tags can slip in many times and be a win-win. Ironically, I have had better luck showing up with a pile of doe tags compared to one. If the landowner has been getting eaten out of house and home, doesn't have a buck hunter booked and you show up and are willing to put a dent in the herd it's not a difficult thing to negotiate. The other thing is to find marginal property that can't get top dollar but still has goats.
The other piece of advice is that some units may have a small amount of public, but it only takes a couple of acres with animals on them to make for a good hunt.
From my experience, I can do all the calling and e-scouting, but to find a diamond in the rough I have to take a chance, buy the tag and go see if there are animals there or not. There is a gigantic portion of WY that has identical terrain and some hold goats and some doesn't. I don't know how you can tell one from the other without checking or talking to someone that has checked. When you are there, try to find time to scout nearby units as well.