Worry less about his SSAT scores. They will take into account the quality of the schools he’s attended, etc. to put that into context. Amazing grades help.
Remember: none of us have met your kid. We have no idea what was in his letter of recs. We have no idea how he presented himself in his interviews.
Yes, schools want diversity. And yes, if a school really likes a particular applicant, they will find a way to meet financial aid. Even if it’s over 90%. And the reason a school likes an applicant can vary. If your kid came across to the AO as a joy to be around, and someone that would make the community a better place to be, that could be enough. They want kids that can dive in and wear many hats!
Also, schools can surprise you. People seeking loads of FA sometimes limit themselves to schools with huge endowments. However, schools with smaller endowments can be very generous if they think an applicant is a great fit.
If the worst happens on M10, look into rolling admissions. There may not be as much FA available, but it’s worth a try.