Are these solos in a big band chart? While I’m not saying it’s not acceptable, it’s not the norm to audition with big band charts/solos. But as a supplement, maybe this is fine. I would call the school and ask. I’ve always found the jazz department offices to be very friendly; the first thing I’d do is to call them and tell them you’re planning to submit a music supplement and ask if there’s a format they prefer/require and if a big band excerpt is acceptable. I would call the jazz dept specifically, not music school admissions.
Are any of these schools you’re applying to nearby? Most schools only have one or two jazz saxophone professors; look them up on the college’s website (music schools always list their faculty) and arrange a meeting/lesson. If there’s nothing nearby, look up the faculty in one of the schools you’re applying to and see if you can arrange a phone meeting. FWIW, I think the only city where my son’s had to pay for a prospective student lesson is NYC; all others have been free.
All jazz “auditions” that my son has participated in always consists of playing a jazz standard in the traditional format; that’s the melody plus improvisation over one or more choruses (depending on the time allowed.) Note that when one says “jazz standard”, it’s different from a big band chart even if the song itself is a standard. Also, don’t assume that they only care about the improvisation part; the “correctness” of the melody matters. As a solo instrument (trumpet, saxophone, trombone, etc.) you would typically want a rhythm section to back you up, or if a live rhythm section isn’t available, a pre-recorded “play-along” track.
I don’t know how much weight the arts supplements have or what their expectations are in terms of level of play, or if you’re planning to pursue music in any manner while in college. These are the kind of questions you should probably discuss with the schools directly. (I’m not a music professional and totally not qualified to assess your playing.)