If you have any sort of choice about where you're moving, it would of course be nice if you could select an area that had many different school choices, because for some GT kids, you may find that what works for a kid one year doesn't cut it the next. But it sounds like there's not much choice where you're headed.
I guess what I would want to know is how flexible a school is. Does the district have a Gifted Coordinator? If so, I'd contact the GC first and ask what their policies are for differentiation and acceleration, and if any of the schools in the district tend to be more flexible than others. Ask if they have experience with kids going to higher classrooms for certain subjects, or if they cluster GT kids together, etc. If you can get the GT coordinator on your side, he/she might be able to help you pick the most flexible and willing principal, who in turn will help pick out the teachers best at differentiation and with GT kids. We went in with scores, and that helped get us the right fit K teacher, but she also wanted to see for herself, so it took a long time to get more appropriate work for our kiddo. (I have one of those kids who doesn't advertise to the world that he is very GT, especially not in kindy.)