Several years ago I organized an effort where a large public property that didn't allow any pheasant hunting but held a strong population, let me trap and transplant wild pheasant to properties in adjoining counties where habitat improvement was underway.
I trapped the birds using corn-baited walk-in traps in late winter. One thing to anticipate is roosters often seem easier to trap than hens. They are more bold, probably require more food, so in some cases roosters became "trap happy" and could be repeatedly trapped if not translocated. I was putting bands on them to help estimate the overall population size in addition to tracking translocations.
I didn't have my own property to release birds onto, so didn't appear self-serving. However, a local sportsman's club covered the costs of my gas and hours. We also asked recipients of birds to "donate" to the project at some nominal level so there was strictly speaking no "sale" of these wild birds. Some landowners received birds if they had very good looking habitat, and even if they donated nothing.
I had a good relationship with the local state game managers, as did the sportsmans' club, so the state didn't elect to require excessive levels of permitting or red tape that could have made the project onerous. If you know of a strong source of unhunted birds elsewhere in Kansas you might be able to organize a similar effort.
