as i understand it, you can (a) run for a non-NLI school (D3, NAIA, juco, some D2, ivy, military academies) or (b) ask for a complete release by the school with which you signed a NLI. if granted a release, you can sign at any school, NLI or not. if denied, you either tough it out or lose the year like a transfer. you do the one year and your NLI is fulfilled.
[side critique: why are they losing a year if normal transfers no longer lose a year?]
i would hand your coach the lousy financial aid offer and ask what are we going to do about this, explain how far it is from reasonable in terms of affordability, and perhaps give him better aid offers from other schools. ask him to fix it, either financial aid office or you need more help. if he can't help, then that is also the groundwork for asking for a release. you basically say, i can't afford that gap, we talked about a far better offer, please give me a release.
you can appeal a denial under extenuating circumstances. that goes to a NLI committee. you'd submit the same sort of stuff, here's our income, here's what this school and others offered, here's how out of whack it is, i can't afford this.
gather up W2/FAFSA/financial aid offers. give your coach a shot. he turns you down, take action, and while you're doing it, apply other places or try and revive the old ones. if you don't want to sit a year or wait on an appeal, it has to be out of most of the NCAA scholarship schools.