Like 100 said, you can hunt in units mostly private (some public) with leftover tag but there's a reason they are leftover. Wyoming has an Access Yes type program where they pay landowners to allow hunting. These are generally walk-in areas. Get that map from WY now, see what leftover tags are availible and go from there. They also have a list of private land (fees) book you can get. I plan on getting it if we draw.
I blew off getting PP's for Wy antelope and regret it. I had to apply for a unit with lots of private and one huge Access Yes walk-in area. May have to pay trespass fee. Points will inprove your odds for drawing an all public land unit or unit with lots of public. Trophy will require more points but it is still too soon to determine how many points a great unit will take since the system is only 2 years old.
I believe Wy antelope will never take many points to draw a good public land unit cause they issue so many tags they'll go through everybody in a year or 2 except for the very best units