You have a good variety of schools in terms of size, location and academic rigor. Visiting the schools and interviews will help your family determine which ones may be the best fit.
Based on going through the process a few times and currently with one in a HADES school and one at a school that has surprised us positively in its academic rigor, the schools will guide you on reclassification. It was encouraged with both of our two children (daughter and son) currently in boarding schools (not with their older sibling but that was 6 years prior) and even though everyone assumes it was because they were recruited athletes, both were strong students coming in and are so thankful academically because these schools are filled with the best and brightest from around the world. One had a summer birthday so made sense but the other a winter birthday but due to Covid it made sense too.
Best of luck!