The problem is that you are trying to find such a school in Brooklyn.
Large Jewish communities are polarized. Brooklyn has MO schools, chasiddish schools, and chareidi schools. There are MO shuls, chassidish shuls, and chareidi shuls. Everybody goes to their box and fits themselves in.
You need to move out of town. Miami has schools like that. Chicago, LA, Baltimore, Detroit, Cleveland, etc.- all have schools like that.