Get in touch with Flat Tops adventures. He does backcountry and has bought a ranch for ranch hunts maybe.
Wyoming has some hunts that would meet your criteria but PP are needed to draw.

RFW, Ranching for Wildlife ranches in Colorado have long seasons and no draw for outfitted hunts.
https://cpw.state.co.us/thingstodo/Pages/RFWParticipating.aspx


Your budget is kind of low but may be doable.