OP, i am saying this with sincerity and concern and as someone who is raising a child with severe, progressive disabilities.
You need to be realistic. You are an adult now. Your parents, even though they are adults, are not being realistic.
You have exactly ONE option and that is enrolling at UMass now.
NEU has rejected you. They will continue to reject you. They haven’t even guaranteed you acceptance to the Boston campus if you enrol somewhere other than the Oakland campus, and they are not offering acceptance after a gap year.
You wrote that you disclosed all your major disabilities including one rare disease, applied only for the Boston campus and they STILL offered you one year at Oakland. They’re not stupid. That was a rejection. They are stringing you along now because they don’t want to be seen as a college discriminating against a student with disabilities but that is exactly what they are doing. They don’t want you. You have talked about your need to be close to an experienced medical provider and they still aren’t budging. Your needs are too much of a risk to them.
The “colleges like students who overcome hardships” myth is a myth.
They may like it when the hardship is over, and it hasn’t made and will continue not to make a difference in your performance. Your disease is progressive. They are expecting to to have to offer accommodations and worry you will not be able to keep up your performance. They don’t want you.
UMass has shown you they trust in you and your abilities to overcome your hardship. They will support you.
A gap year does not mean you get a do over. You have already worked with the Broad institute. Your high school record is what it is. I am not sure you can take the SAT once you’ve graduated, others may want to weigh in in that. It will not count once you are a transfer student. Your application will not change meaningfully, you will still look like a risk to all the private colleges you have rejected you before.
Your parents’ instinct is to grab for the one “offer” that isn’t really an offer, but is somewhat more highly ranked, and to keep you close. Don’t give in. You have said yourself that college may be the one thing in your life that is normal, but it will not be if you start messing around with the one option you have.
You have not disclosed your disease, and you don’t have to, and do not need to give us any more information. But you need to think about this. You have let us know you are already Deaf and may be going blind. Should you waste another year not getting to know the college campus you will live on?
You have hinted that you are genderqueer but closeted. Do I understand correctly that you are currently presenting as a woman, but wish to live as a man, and your parents don’t know?
Do you currently wear the hijab and are you planning to ditch it on campus? You don’t have to answer, but you need to think about it. How would that work if you still lived so close to home? Again, UMass now may be the one chance to understand for you who you are and who you want to be, and to try out how to live independently.
Lastly, it does not seem to be clear that your parents can pay the additional 200k NEU would cost. Another huge risk. And one your parents do not seem to appreciate.
You must make them understand that neither a gap year nor NEU are an option.