You might consider, if you move, looking for an area with a variety of educational options. You may get lucky with a great match at the first school, but many of us have had to change at least once. Flexibility can be helpful.
Given that you plan to have your children involved in activities like 4H (great choice for many reasons) and soccer, I'd not worry so much about the perceived value of "normal" interactions during the school day. Everything outside of school provides an opportunity to interact with many types of people, and that's especially true when parents are sensitive and trying to make sure those interactions happen. I think sometimes we overvalue this as a benefit of a traditional school environment and forget the real downsides for a highly gifted child. Things like bullying, standing out too much, over praise for things that come easily, lack of learning to wrestle with learning challenges, feeling like there must be something wrong with you because you are so different than your classmates, trying to fit in and dumbing yourself down to do so (especially a concern for girls). I'm speaking from personal experience as well as research I've come across. :-)
Before you move, however, have you fully explored the various options in your small school? Sometimes a great deal can be done if the administration and teachers are flexible.
Regarding this concern "The world is not filled with gifted kids, and I worry further that there is an "institutional" effect, where GT kids get so accustomed to the postive feedback loop of a GT school that they find themselves unable to function well without it - which is to say, in the real world, no one is giving you grades for how well you do on tests, right? (Unless you remain in an academic environment.) You need to be able to succeed outside the academic world, too."
I would consider whether this is a real issue for gifted programs, versus what happens in any school environment that is heavily based on how one does on tests and assignments. I would say that this happens for a gifted child in most school environments (or any child who does well in school) and is a larger societal issue. Speaking as someone who has seen this as a transition challenge from college to the working world for many new hires, none of whom went through a GT program to my knowledge, but all of whom were top students.
