I hear patterning a shotgun is as important as zero'ing your rifle.
Not quite. Patterning your shotgun might be mildly interesting, and should give you some idea of your realistic killing range, but with a full choke and good loads I can tell you it's going to be 45 yards give or take 5 each way. 6s will pattern better but carry less energy at range. 4s will carry better energy at range but pattern worse. I've used and killed turkeys with everything from 4s to 7.5s. I usually use a high quality 5s.
The thing about patterning isn't that it's going to hurt you, it's that there are several other things you can do that will help you kill a turkey more. The most obvious, particularly in ag country like most of Kansas has, is to scout. Turkeys are very patternable in ag country. If you see a tom strutting in a given place at 10am there's a good chance he'll be there again tomorrow. Better yet, figure out where they roost, where they feed, etc... String all your info together and you'll generally be able to kill your turkeys without needing to be able to shoot past 30 yards.
Calling, bird working, building blinds, feeders, land owner relationships, scouting, even basic woodsmanship will all be activities that will help you kill more turkeys than fiddling with chokes and loads will.
Where in Kansas are you going to be hunting?