CAR,
What do the contract terms say with reference to release of liens? You were right to attempt to settle, this is always the best way out if at all possible. Isn't mediation mandatory as the next step? IMHO you need a lawyer familiar with contract law if you haven't already done so. I've not directly managed any construction contracts in Florida but I was directly involved in settlement of a fairly large construction related dispute. The laws are different state by state. Usually I've been able to force them to provide proof of damages (receipts, shipping and delivery, bills of lading etc).
Did you finish with a different contractor or are you required to clear liens before that can happen?
So sorry you're having to go down this road.
I hope this is helpful.
Chris