Is there any WY hunting forums? Lots of state have them. Some forums have areas dedicated to certain states too. Not saying to go some place else, but some place with more WY traffic may help you out.
Also never know if people want to give you to much info on where they hunt. Though being a transient in the military they may be more helpful.. People will often give general info either way.
There are maps you can buy for Garmin that tells you property is public and private. Xtreme hunt maybe. Cabela sells them. I once bought book from sporting good store and wrote in it while talking to clerk.