So I found what might be the perfect school - even if it doesn't have rugby or fencing. It's halfway between Philadelphia and New York City, and it offers the following courses:
Forensics I & II (science credit)
Detective Fiction (English credit)
Urban Architecture (math credit)
I mean, come on! An architecture course for math credit? How awesome is that?
Also: The New York Military Academy offers Forensic Science. That's kinda cool.