Time for my "equity plan" for handling the situation
1) The woman has the legal right to decide the pregnancy at any time. If the woman wants an abortion, she can get one.
2) When the woman discovers she is pregnant, she has two weeks to notify the father that she is pregnant.
3) Within 2 weeks, the father must declare his intent to provide support for the child or not support the child.
4) Armed with the information from the father, the woman decides whether to carry the pregnancy to term or to have an abortion. If the father declared to not support the child, and she has the baby, then he does not have to pay child support but he also loses all legal paternal rights. If he offers to provide support, and she decides to abort, he is SOL. If he agrees to support the child, and if she carries to term, then he has legal rights as a father, but he also has to pay child support.
Assuming that the woman discovers she is pregnant no more than one month into the pregnancy, this plan means that the fathers decision must be received by 2 months, still within the first term, allowing plenty of time to abort if she wants to. There probably should be restriction on how long the mother can wait before contacting the father, so that she can't wait until the third trimester before verifying she is pregnant (and it would encourage the woman to get to the doctor early on).
So here's the key to the plan: Ultimately, the decision for the abortion is soley in the hands of the woman. Her body, her decision. However, it is an INFORMED decision, and her decision is based on his willingness to pay. Moreover, she does not hold unilateral control over the process, and he is not controlled by her decision.
The biological difference is covered here. He cannot force her to have the child if she doesn't want to. Similarly, he cannot force her to have an abortion if she doesn't want to. She has control over her body, but he retains control of his wallet. SHe just knows when making her decision whether he will be providing child support.
ETA: I forgot to mention, missing deadlines will lead to implicit acceptance. I.e. if she doesn't notify the father in the proper time, she foregoes any right to child support. If he does not respond to her notification, he is bound to pay.