You don't have a basis for an appeal. Really, this is a discussion to have had last year, not now. As your various parentals have told you the facts (that only your bio mum is on the hook for your college $) then applying for expensive schools was a mistake. No schools with CSS/profile will give you FA, your only escape route was merit, did you leverage that?
Plenty of married parents won’t pony up for full pay privates, let alone divorced remarried units. Your situation more common than not. Any CSS/profile school will consider your various income revenues.
What is your home state? What other schools have you applied to that won’t require FA? What are your stats?
The cost always going to be full pay, did you talk to adults about your applications? Did they give you a budget? Your bio dad is not contributing anything for college (or how much will he contribute)? Do you not have a relationship?