@badminton4life The “top” boarding school really depends on fit for the student. There are about 50 ( some would say more) where you can get the type of education that few students in the US have access to—incredible classes, facilities and support. They are all so great that you can attend any university and do exceedingly well. I often see on these boards people applying to the same name schools. As someone who knows many graduates of various boarding schools, there are a number of schools whose names don’t appear as often. These schools rank the same as those you mentioned. They are just as difficult to get into and offer impressive graduates. So you might want to expand your thinking and rather than going for the same 3 schools, look at those in the top 25 or 50.
In terms of your original post, there are many “repeats” I think parents and students realize that starting in 9th grade has definite advantages.