That is a thorough response! First, I googled you and watched the trailer for your film, 45 RPM, and the fact that this is a feature and it is beautifully executed means you should keep this up no matter. Suffice it to say, I was humbled. Thought to myself: this woman has vision. It's no wonder you got accepted at Columbia University. You didn't elsewhere?!
Sorry to hear about your financial aid challenges. And it gives me no pleasure knowing a spot will open if someone as talented as you cannot get the aid she needs to attend. Frankly, I'll be in a somewhat similar boat but, maybe, being an older student with a longer history, I would be okay. I'm still cautious. Also have a patron who might help. Might is the operative word. It's a racket, tuition costs and financial aid.
I think you should definitely contact the financial aid office, research personal loans, and contact your patrons. You might be surprised how much you can cobble together. And know that once you are in it is easier to find more opportunities for aid via grants and scholarships. I'd say look at it as a long game. Someone like you would go far in a program like this so it's certainly worth the uphill climb.
As for my/mr. wanderers, etc. chances, guess we will see. I do know that they went back through the list and reevaluated everyone from scratch which means you were probably one of their first choices. In all likelihood, you were probably close to getting in on the first go around. I think you definitely should go whole hog re-applying this fall if you cannot rectify things now. Apply to a bunch of screenwriting and directing programs as I'm convinced you will not only get in, you'll get the money. Hell, I'd even double up and apply to screenwriting and, separately, directing at certain schools like AFI, UCLA, and UT Austin. Dollars to donuts, things are going to work out.
Be curious to know about your experience at NYU re: writing a continued interest letter. Only reason I wrote one for Columbia is because they suggested it as an option when they responded to my inquiry about submitting additional materials, like more recommendations or films, not being an option. I had sent the electronic reply about remaining on the waitlist a month or two prior before coming around to writing a formal letter of continued interest to Dean Rossi. Hoping that I came across as humble, confident, and interested. One worries it comes across as presumptuous. Hope it helped rather than hurt my odds.
Anyway, I wish you the best of luck because you deserve it. Definitely continue to share your stories about this process moving forward. I started a post about being on the waitlist a few posts ago.