My dad took us to South Dakota and Nebraska more than once on DIY pheasant hunts when we were kids.
Didn't have any dogs. It was fun. We killed birds.
That being said if you could find something in the panhandle of Texas that allowed trespass or daily rates, you might be miles ahead. Some of the best COCK hunting in the country believe it or not. But private access is the name of the game.
Travis