1. Provoke the other side. Constantly. Women who have the courage of their convictions about abortion and are willing and able to bear the expense and risk should make a spectacle of having them, and provoke the fundies as often as possible, as egregiously as possible, while remaining within the sense of good taste that centrists mistake for morality. Show in action the zero-sum position that fetuses have no inherent moral value and can be aborted with no greater reflection required than to remove a wart, because the absolute reality is not very far away from that - a fetus has the moral value of any other insentient life, like a fish. And you might be morally upstanding enough to have a problem with killing fish, but for the sake of the rights of humanity, pretend that a fetus is nothing.
2. Draft doctors. Solicit qualified doctors who are on the record as favoring abortion rights to perform them at least part-time, pro bono. Shame those who fail to do it at least once a year. This increases the number of people on the fundies' target list and thus makes everyone on it safer.
3. Technology. Radically lower the cost, improve the safety, and reduce the preparation/recovery time needed for abortion. A general abortion pill or a safe and effective home kit are at least theoretically possible, so invest in research toward those ends. Also support research toward mobile equipment that can safely allow a doctor to perform abortion in a patient's own home. I don't know if any of this research is underway, but if abortion is your issue, ask about it and push for it.
4. Mobility. In fundie states, abortion has to be approached like a guerrilla activity to some extent because most women will want maximum privacy. So get mobile abortion clinics legalized in some Blue state, and then make hit-and-run attacks into the fundie states even if it's illegal there. Or you can just run pro bono transportation services to bring the woman to where it's legal, but that lacks the benefit of civil disobedience. The rights of women trump the privilege of fundies to control them, so either service would be like an underground railroad sort of thing. Bring the women to the clinics or the clinics to the women, but however it's done, maximize the availability and minimize the time and effort involved.
5. Promote Fearlessness Among Women.
Educate women about the social benefits they can provide by openly having an abortion and publicly talking about it rather than doing it privately. Most would still choose maximum privacy, but some might decide they owe it to society to stand up concretely by talking about their abortion rather than just supporting the abstract right.
6. Promote Pragmatism Among Men.
Child support. Garnished wages. A mother who moves far away so that you can't see your kid while still making you pay. Is that what you thought of when you imagined your future self as a father? A cash register for someone who loathes you to spend on someone whose life you're not involved in? It might have been different. You might still be free of these financial burdens and the disillusionment of being turned into an anonymous meal ticket, if only the alternative had been more available to her. If only she had known her options; if only you had been willing to pay and help her out with that one procedure; you wouldn't still be paying. Have a real family - a planned family - not some stranger who's taught to hate you while your paycheck feeds them.
7. Recruit the family members of fundies and GOP politicians to publicly have abortions.
This sounds mean and personal. It is. But remember that they shoot people, plant bombs, and turn women into state baby factories. And maybe, just maybe, they'll learn some damn humility from it.
And then the obvious stuff: Greater sex ed, expand access to healthcare in general, and so on, and so on. But abortion rights people really need to get on the ball and seize the moral momentum. Don't just get in a tizzy when the fundies are launching an attack - you need to be on the attack. That's true no matter what your issue is. Stop fighting holding actions. Expand what it is you support, don't just be forever building Maginot Lines.