Applying only three could be a sound decision, if one has good local option and mainly cares about better academics, rather than the boarding experience. Actually for me the latter was a concern rather than a reason for applying.
I would rank the determine factors(either positive or negative) in your case by orders as: Asian Female > NJ > Art and other extracurriculars( only if they are good enough) > past curriculum content/school > grade > SSAT > essays > interview.
The reason for the first two or three is that they decide in which bucket of candidates pool you are compete with. Since you did not mention anything spiky or as hooks, this bucket classification become crucial for the final outputs.