It's mostly the poor and uneducated who are so irresponsible as to wait until the third trimester to seek an abortion. I'm not sure that laws banning legal abortions during this period would have any effect on such people. They'd just return to the coathanger-butcher era.
I'd like to believe that education and easy availability of both abortions and contraceptives would help but I'm not sure. That's where we need real-life experiments in various states - or perhaps there is already good evidence and I'm unaware of it.