How can I improve my application?

Hey OP, try to give yourself at least three months to study. That way, you won’t have to cram the material and would find time to study at your own pace. The upper level SSAT is, in terms of content, much more challenging than the middle level SSAT. While it is impressive that you scored in the top 16% in that level without studying, I don’t recommend going into that testing center blind again.

Just to throw in my two cents into this SSAT debate (not that it was asked for but I just couldn’t resist) I could see a score in the mid to high 80s harming an applicant if another applicant had a similar “resume”, along with a much higher score. Also, applicants such as I, who are applying for full aid and aren’t really anything too special, should try to get a score above the 90th percentile. It’s already known here that needing aid is a disadvantage. No need to disadvantage yourself further by getting a way-below-the-average SSAT score.