I think CTLAWYER is right — a lot of OOT schools, especially in small communities, will accept pretty much everyone, regardless of how much you can pay, your level of observance, your academic aptitude, etc. (unless there is a severe disability they can’t accommodate or something).
Chabad community schools are known for taking everyone. Perhaps this is a task for the next generation of shluchim looking for something new to do — start high schools that will accept those who get rejected elsewhere, but which are run in a way that is acceptable to Yeshivish and other non-Chabad families?
Rabbi Shais Taub’s column in Ami last week was about this issue, and if I remember correctly he basically suggested that schools should accept everyone, even if it seems they might not have the room or the resources needed to help that students, since after all schools are meant to help individuals, not to help the institution itself.