Custody considerations?

My stbx and I were together for a year, and were married for six months immediately after I became pregnant. During the pregnancy he became increasingly unstable and abusive, refusing to let me out of the house and beating me. I left before my son was born, and obtained a restraining order while my son and I were in the hospital. As soon as he was served with the restraining order papers he filed for custody, I took out assault charges (which he admitted to during the trial, although the photographs of extensive bruises were plenty of proof), and he now has one hour supervised visits once a week.

I am currently good friends with an ex-boyfriend I dated for five years before my stbx, and am considering moving on with the relationship after the divorce is final in a few months. He has been very good to my son and I, helping my family with him while I work, seeing him several times a week. He has also helped us out financially a great deal, and has been involved since I left my stbx (he found out what was happening and helped me escape, and was present in the hospital when my son was born). He is the kind of father my son deserves and the kind of man I deserve.

My stbx filed child abuse allegations against me after the supervised visits began, falsely alleging that my father is a pedophile. The investigation was fairly pleasant and over quickly - they believed us, since there was OBVIOUSLY nothing going on and the allegation came immdiately after my father refused to give my stbx my contact information. I am afraid of continued false allegations.

The divorce will be final in October, and my son will be a year old in December. My stbx wants weekends with my son once he’s a year old - but since he beat me, has a self-professed anger management problem, had two daughters taken from him five years ago because of his abuse against them and their mother (and criminal charges from that as well - but the records were purged because the state they’re in does that, although we have confirmation that his rights were involuntarily terminated), I’m concerned that he will hurt my son. He also has no proveable income, since he’s working for cash and not paying taxes, so he refuses to pay child support and has made no effort to provide for my son in any way.

I expect him to retaliate once he finds out I’m dating (this username is fake, btw), especially when the restraining order expires soon and especially if my son and I live with my partner (I have been offered a better job in my partner’s area, starting several months after the divorce is final, and it only makes sense to live with him eventually).

What can I do to protect us? Since I cannot have his rights terminated yet, I would prefer to keep visits supervised - but he’s been “on his best behavior.” How can I have psychological evaluations conducted, and home evaluations (he has had no permanent residence since I left) before unsupervised visits are considered? He is very manipulative and good at playing the victim, I’m afraid of his leverage against anyone evaluating. I know I may have to expose my son to harm until he finally messes up and hurts him like he hurt me, but isn’t there something I can do?

And how can I reconcile my desire to provide my son with a loving father, without “looking bad” in court for becoming involved so soon? What factors should I be considering, and what should I be doing (or not doing)?