Academically you seem qualified, based on your GPA and assuming you get 95% or better on SSAT. But for the schools you are applying (PA and PEA), academic qualification would only put your foot on the door. That is the only problem. They seem to demand a very strong hook. In order for an academic to be a hook, you need to win some unusual recognition beyond the usual such as doing well in school and acing tests, since almost every apolicant is an A student. Ask this to yourself: why should they accept me? Why am I a compelling candidate? “Compelling” is the key, since 90% of applicants get rejected from those schools.
I am sure you know that the schools you applied are not the only good schools. In fact, I would think, out of the whole, very limited profiles of students would be great matches in those places. There are many many choices between the public school whose resources you seem to have exhausted and the two schools you are applying; it’s not an either-or proposition. Have you thought about other schools too?
That said, since you must have applied already, there is little reason to get nervous about it. And I would definitely apply for FA - especially since there are 4 kids in your family. In calculating your family contribution amount, they take that into account. It has always been my belief that no school is worth going while breaking someone’s back.