Tulane does not meet full need for most students. They say they give less merit in the ED rounds, but some people do report receiving enough aid in the ED rounds.
Tulane is a CSS Profile school, so will require bio dad’s financials. Have you run Tulane’s Net price calculator to get an estimated cost? You would have to include your ex’s financials in that (and any new spouses) for that to be accurate. It may also not be accurate if there are other complicating factors, such as a parent owns a business and/or real estate beyond a primary home.
Lastly…you can break the ED contract if the FA package isn’t affordable, but obviously that’s less than ideal.