SSAT scores go against my narrative

No, you will be fine. I am assuming you are a girl, from the grade split. Those are excellent scores, and no need to worry. Anecdotally, many strong math kids seem to do very well on verbal. I conjecture that the same instinct for systematizing information helps strong math kids to absorb grammar rules and to note subtle differences between primary and secondary word definitions without even realizing it.

However, I will caution you about your math progression if you are still in 8th grade and are taking calculus. Few high schools can provide you with meaningful courses a year or so beyond AP Calc, not even some of the most prestigious boarding schools. Once you are accepted, have a frank conversation with the school on how they can accommodate you, and do not just accept assurances that they will find a way. Of course, if you are willing to go back and do algebra and geometry all over again, this will not matter, but it will be a long, boring slog if you take that path.

We have been exactly in your place with an advanced math kid, so feel free to ask any questions you like.

Good luck!