How is that relevant? In your preferred system, that would only happen if the man wants the woman to have the child.
As for the decision time, I'm thinking of it like unemployment benefits. Suppose a person has just lost shis job, and has up to six months to find a new one. During those six months (or until se gets a new job), se will receive regular unemployment checks for a steady income. What is this person likely to do? If se does not have a job already lined up, or readily at hand, se is likely to dawdle for five months and then get a job just before the checks run out.
The same would happen with a lot of the pregnancies. If the father is initially unsure of what he wants, he will have little incentive to make the decision until the deadline is looming. A lot of mothers would end up having to endure pregnancy for a long time anyway, just waiting for the father to choose between abortion and child support. I see this as unfair, and potentially used as leverage. It could be pretty well remedied, however, by establishing a certain cost to be incurred upon the father (to help cover the mother's medical expenses, with a little pain-and-suffering bonus), which would increase with each passing week that he delays his decision, so that his incentive to hurry it along increases just as the mother's discomfort is increased.