If father refuses to sign custody agreement, but refuses to get a lawyer, what then?

My daughter has been in my sole physical custody since the day she was born with her father being very hands-off. Recently the state of Louisiana filed child support enforcement against him because I am in school and she is on Medicaid (standard operating procedure). I haven't heard from him in two weeks and this is the first time he has been forced to do anything with her, usually he doesn't ask about her or keep in any contact at all. At this point a lawyer is writing up papers for sole physical and legal custody to be granted to me. He says he will not sign them if he is not granted 48 hour every other week overnight visitation. I refuse to give him that because he has a male roommate and his girlfriend living in the apartment with him. Secondly, he is very negligent of the child he has custody of, even to the point of CPS being called. If he refuses to sign the papers he cannot afford an attorney (he is unemployed) and said he wouldn't pay one regardless. If he does nothing in regards to the agreement is there a statute to the time in which it will be basically in limbo, or is this going to be left to his whim? I know if I go to court I am required to have a joint custody agreement written up "just-in-case" but I refuse to let him have custody of her because of his abusive and neglectful nature. I am absolutely no going to budge on that matter.