I won’t tell you to not try an appeal, but there is nothing in your OP that is a compelling reason for a change.
FAFSA is used to qualify for government financial aid programs…pell grants, Direct student loans, federal work study, etc. It is not used by (most) private schools to determine one’s need.
NYU uses the CSS Profile to calculate a family’s expected contribution, and then tends to not fully meet that number (except with loans).
Choose a college that is affordable for you/your family. Do not take out undergraduate loans greater than the $27k total allowable direct student loans.
What is GT’s net cost? Do you have other affordable options?