The abolitionists created a bill that would put most of the slave traders out of business without directly voting on trade itself. The abolitionists regulated the bulk of the slave-trade out of business.
The Virginia legislature has found a similar route to help end abortion in the state. The legislature passed a law that requires abortion clinics to comply with same regulations as hospitals. From the Richmond Times Dispatch:
Under the legislation, any physician's office performing five or more first trimester abortions a month would be classified as a hospital, subject to special regulations established by the state Board of Health within the next 280 days.
The abortion lobby will certainly challenge the law in court. But the chances are far better that a court rules in favor of a health-facility regulation than a law restricting abortions in the first trimester.