@ThePhoGuy You have an interesting background for the application but, yes, SSATs are HUGE for these schools. I personally recommend buying the SSAT.org study materials. I found them a better value than the independent guides. My own son had to prep for the Mathematics portion. We also used the SSAT.org materials with a Math tutor (the English side was fine for him) once a week for six sessions or so. It made a big difference to tackle the high school level concepts he had not studied.
All of the schools you mention are essentially 15-20% acceptance rates WITH 90%+ SSAT scores. Expanding your reach is also a good idea. Your resume (outside SSAT scores) would be interesting to many, many schools.