Get some legal advice, but it seems to me that if you are divorced, and she signed away physical custody, and you have a legitimate financial need to move, I would just do it and let her pursue you afterwards. (I'm assuming you have a job that you can easily move locations for?) She's unlikely to win. And it will take time for her to pursue it if you have already moved. Maybe as long as you were planning to stay there anyway.
I'm sorry about the divorce debt. Check out the Mr. Money Mustache website to get inspired about paying down debt and getting financially squared away.
Sorry too about the touch-and-go. It's rotten to get your hopes up and then have them fall away again. Best advice is to just get along with your life putting your kids and your own needs first. Let her have her experience. Get busy living life. If she ever comes around to her senses, you can decide THEN whether reconciliation is something you want to do. But for now just get out and live life. (Check Irish's thread on the MLC forum for an example of a man doing a great job raising his daughters with an absent WAW.)
