You are in a catch 22 that is not going to improve with time.
At any point in this process he could stop paying for things and disappear.
No matter from which point you start it will take 90-120 days, so why are you waiting.
He is NOT going to get nicer and more cooperative the longer this goes on.
When you have a job and income you will get less in support. Yes he can seek to modify later, but that takes time and money.
You can put on your charm and give him the choice, does he want to come to an agreement (which you can present to the court) or does he want to battle in court. That you are just taking this step to protect everyone and to make things clear to cut out the potential for conflict between the two of you.
I also live in a no fault state (as do most folks these days). My H is the only one on the note and we are both on the deed. I told him to leave. He said he wasn't leaving and it was his house, blah, blah, blah. I told him I would get a kick out order to have him removed. He ran out of the house like a scared chicken saying he had to work an overnight shift (which he had never done before). I drove to her house, took pictures of his car outside. They saw the flash and I saw them inside. He had blocked my phone so I emailed him and told him to come out. When he did I told him I wanted the key and garage remote (he had already shown up once in the house when we were out claiming he wanted to start over).
My point, there is law and then there is reality. If you tell him to get the h*ll out and don't come back, he will probably do it. First try to be charming and get him to agree to pay you a specific amount of support and agree on certain visitation (FL probably has a standard for the non-custodial parent). If you have a contract he will be less likely not to pay in the 90-120 day period and that hearing should be cheaper and easier because of the agreement.
I think you are afraid of pushing him further away. Too late for that. Train's tough love approach will serve you better than being nice or weak at this point.
The only thing I have going for me now is that my H is scared to death of me (and I set the mortgage to pay after he gets paid--no money in my account and I don't pay it--guess who takes the credit hit).