You CAN'T do this.
Even IF you could prove abandonment by his father (which, as you have stated he is paying very little, thus indicating he is paying something...ie: NOT abandonment) the fact is that NC will look at the fact that the child is with a relative (you) and could very easily determine that there is no reason to terminate parental rights.
Let me tell you a little something about NC. The court in NC will give a parent every shred of a glimmer of opportunity to develop a relationship with the child...even IF the parent is a complete loser.
Forced termination of parental rights based on abandonment by one parent to facilitate a step parent adoption is very, very difficult. I personally know of another person going through this and the ex makes yours look like parent of the year. They've been trying to terminate parental rights for 5 years now so that the step can adopt. The reasoning is that the child is not in any danger, is not neglected, etc. The child is already in a perfectly stable home and wants for nothing (the child lives with the father and step mother ready, willing, and able to adopt).
If you ex doesn't consent, it's a one in a million shot. The fact that you are already engaged to another man who your son refers to as "Daddy" and you are not even divorced is going to be a HUGE FREAKING ISSUE when you get to court. A man doesn't have to legally earn the right to be called "Daddy". He accomplishes that feat by depositing sperm, fertilizing an egg, live birth, and establishment of paternity. Paternity was immediately established by your STBX because you are married to the father of your child. It's not the court's fault, your child's fault, your fiancee's fault, OR your STBX's fault that you were so weak in the decision making department that you thought it was a good idea to make a baby with this person. The ONLY person at fault is you. You don't get to make the court clean up YOUR mistakes.