you have to check your unique situation
for the 100% custody issue. first, you need to figure out what is best for your kid, as some mm mentioned below, kids need their father figure.
Honestly, I don't think you and your LG is issue is in the custody, it is the $$ associate with the custody.
ask yourself this question, if he won't not pay a penny for child support, but you have 100% of custody. would you still accept it, and still willing to give him visitation right?