There are many VI Form/ VII Form FP applicants ( day students and boarders ) applying from nine other JBSs ( there are ten ) with similar or much better stats. Then imagine or add all the applicants from PDSs from all around the country / world that will round out OP’s pool.
Then look at the school list and the stats again. Not an athlete and the ECs are fine but just okay. People here might see the wonderful SSAT score and think- WOW! but TBH - I’m thinking- so what?
The line forms to the left with that score and academics isn’t everything.
Plus- depending on the schools we’re talking about ( which JBS to what SS ) the SSs above aren’t known for taking large numbers of kids each year from any one JBS or Private Day school. Milage may vary from year to year - school to school ( of course! ) but the number is usually on the lower side - even though that is never written in stone.
Enter EVERYONE rolling the dice to a certain degree and the very reason why JBS/PDS parents and their kids DON’T talk about their SS apps or share their apply to list with anyone ( outside the placement office ) during the process .
We applied to SS from JBS three times and even though my kids were accepted to their FC schools, no one ( and I mean no one ) thought our pool or our apps from a JBS were a home run or somehow an “edge” on the other competition - especially without a viable option at home. It’s also important to note that the vast majority ( 99% ) go on to SS- BS from JBS and PDS applicant SS- BS numbers are larger today than they’ve ever been.
I’m fully aware of all the JBS perks and always onboard for a little JBS chutzpah, but come on! It’s not exactly a pool I’d wish on anyone. 
Go Big or Stay Home apps are what they are ( there have been sad sonnets written post M10 from a large number of casualties over the years ) so again - TBH- I’d give each app above 50/50 ( at best ) in that pool w/ that competition.
Obviously, I hope I’m completely wrong in this particular case, but unfortunately I’m being a boarding school realist right now for all the future applicants who will one day read this thread.
In sum ( and this is NOT directed at the OP ) : Never target a school or schools based on grades or one SSAT score. One score should never dictate which schools you apply to unless you want to go big and have a viable SS option to fall back on at home.
Anyway- fingers crossed, OP! I sincerely mean it and I hope your DC gets one or all on M10. Good luck!!