UPenn has the graduate fellowship program you mention. I think it is the only program in the country that places student teachers at boarding schools.
It is a pretty neat program. Kiddo got to sit in on a class taught by a fellow at NMH when we toured, and it was ah-mazing. But no doubt, that can vary from fellow to fellow.
ETA: one of the reasons we looked at bs to begin with was the tutoring culture at our lps. Many top students had tutors, not to keep up, but to get ahead. There are 2-3 local tutors who have the book and the syllabus and teach a section ahead. And then you have to get the separate writing tutor, private music teacher, test prep service, and college counselor. And therapist. And sports coach. On top of the club team. Doing the math, bs is not that much more expensive and seems like a more sane life balance - for the parents and kid.