Outlaw abortion but ask everyone in the us to register as pro life or choice. All the new born babies will be awarded on a lottery basis to those registered as pro life.

This is assuming anyone on the list could be asked to be moved to the top.
No, it'd have to be a true lottery where unwanted babies are forced upon pro-lifers, so that if you're going to declare yourself pro-life, you also have to be willing to take on caring for babies who otherwise would've been aborted. I figure that would leave room for the good Jakesies of the world to then market themselves as being extra willing to take that on and have the pro-lifers-that-aren't pay Jakesie to adopt the kid rather than the current system where Jakesie has to pay to do a good deed.
Of course, if under the threat of having to pay money or take on more responsibility, a majority of people aren't pro-life, then abortion should be legal for all. Wouldn't this work? If you're so committed to the position and want to impose it on everyone, you have to accept the possibility that the "burden" (I'm aware some won't see it as a burden, and will thus profit on this) could fall directly on you.