I'd propose a compromise where abortion was legal after posting a public notice first with the father being named also. Sorta like when you declare bankruptcy you don't get to do it in private with no one knowing. Maybe make them post a big sign in their front yard like we do when people ask for rezoning of a piece of property. Unborn children deserve at least the same amount of recognition that they're getting shafted as creditors. Irresponsible momma still gets her vacuum tube, she just won't be able to hide and pretend it never happened.
What legitimate government objective would be promoted by publicly shaming women choosing to receive a legal medical procedure and how would this not be an egregious violation of HIPPA?