I have read the OP 4 times now, and it's not getting any less sadder than the first time.
If I can butt-in and throw a suggestion in here, I will. If it's not welcome, I can always delete it.
In my opinion, you are right. I too believe that all children have the right to know who their parents are. A child only gets one mother and one father in this life. If you prefer not to have your child's father named on the BC and he doesn't want to sign the AOP, may I suggest photos that you can share with him/her later on?
While it's true that absent establishing paternity, you will not have to ask him for anything regarding your child, in regards to passport, leaving the country with your child, etc, establishing paternity would at least allow your child to know with 100% certainty that this is "Daddy". (Not implying that you would just make this up).
I was separated from my father after he and my mother divorced, and no matter how angry I was with him for leaving, later on in years, I wanted a relationship with him. Not all children are the same, but most are, to the point they eventually want to have a sit-down with the parent to learn about them.
You are handling this much better than anyone I've ever seen post on a forum before. I applaud you at your efforts in doing what you believe is right for you and your child.