I think you should a submit a SSAT score for sure. Try and take the test again but submit your 70 if it isn’t higher and be proud of your score as a non-native speaker. It is a difficult test and you are being compared to a very competitive pool. I think it puts you in a positive light particularly compared to a more general English score. This not a 70/100 at all.
If you don’t receive an acceptance or enough aid, it won’t be because of the SSAT. There aren’t enough spots for highly qualified perfect score / full pay kids. Boarding schools build a class to fit their unique needs.