All comments and criticism are for the point of helping, not hurting your feelings.
Couple questions:
1. Define early?
2. Are there any state schools that may have taken a closer look at you? All the schools I was invited to interview at besides one was within my region (midwest, etc.) of the US.
3. Are you able to look at your letters if you officially become a reapplicant? I heard one scary way to sink an application is a bad LOR.
From what I can tell, you're strong and must have slipped through the cracks. A lot of these schools have high volume applicant loads I think. I can't put a finger on it but I bolded the schools I applied to who did not send me so much as an email for my application (and it they did, it was a silent rejection where I had to check my portal). Underlined are the schools where I heard things from and received good correspondence. TBH though, I don't know what to tell you.
Have you considered contacting Rutgers, RWJ, the New York Schools, etc. just to express renewed interest? I contacted a decent mid-tier school I'd heard nothing from saying I really wanted to interview there (it was one of my top 3 choices given the region, ranking, and cost) and two weeks later I got the last interview day before the waitlist started. I say if you want to go to school now, contact Rutgers and tell them you weren't accepted anywhere, would love to go to their school as you have personal connection/family in NJ, and they are your top choice. If you want to take this as a chip on your shoulder, take a year off, and apply to even better schools next year like many do, start planning that out. Also, I know they're pretty prestigious but why didn't you send your secondaries to Einstein/NYU! Come on man, every school counts and you had the summer to churn out secondaries, did you not?