Thanks, Scott. I was considering the Katy Trail, but then I read several post about how many flat tires people had due to thorns from trees and the limestone base being washed out or hard to navigate on smaller tires. Should we not be worried about that?I haven't ridden the Katy so I can't add any Katy specific info. That said I will say this... It depends on whether you personally would enjoy the Katy more than riding on the roads. Personally I avoid bike routes especially unpaved ones. If road touring I'd rather ride the roads. Some people love trails like the Katy.
It looks like the Katy is a reasonable options if you like that kind of riding. Otherwise stay on the Trans America until Chester, IL (home of Pop Eye). BTW, other than the fact that it was over 100F when we were there, we enjoyed stopping for a while in Chester IL.