You have to remember that HMHS was created to provide a safe place for gays where they would not be teased and bullied. I think the obvious next special high school would be for geeks and nerds.
Unfortunately, such a school would wreck the grade curve for science and math. They would also have to teach English as a Second Language there.
Shalom.
I thought they already had one -- Stuyvesant High School! (rimshot)
Illinois has a school called the "Illinois Mathematics and Science Academy", a public high school for students gifted in those two disciplines. It's an hour or so WNW of Chicago. It has competitive admissions; any Illinois high school freshman (it has sophmores to seniors only) is welcome to apply.
It has sports teams, etc., just like any other Illinois high school. They generally suck. The math team usually wins the state championship, though, even over the various excellent private schools in the Chicago area. They have many students that excel in the fine and performing arts and foreign languages as well (the latter partially explained by the fact that many of their parents were born in China or Japan). Many of them also get involved in community work.
I had the privilege of interviewing half a dozen of their seniors last fall for the purposes of supplementing their admission applications to MIT. One kid I interviewed had placed very highly in a national math competition, had co-written an instructional book on Go with her mother, and was runner-up for Miss Teenage Illinois.
Nice to see that the top students are getting some of the money and attention.