To me, wanting the boarding school experience would mean targeting a much broader range of schools than the same two top schools that you’ve already considered.
There must be dozens of other schools that could offer an amazing experience and that you would have a much better shot at for admission.
If, however, your view is that your experience should be at “the best” or nothing at all, that’s a common (though I think grossly uninformed) perspective. But even in that case, why not apply to a different cohort of “top” schools than the ones you’ve already tried?