Your arguments are sound, but I think the bottom line will be economic, not ideological.
If this dog (successful lawsuits) hunts, the women who've killed their children will pursue it.
And so will the lawyers.
Everyone involved will rationalize that, 'yes abortion is a sacred right, but I'm justified in my action because...'
At some point the radical pro-death infiltrators in the government will have to move to protect their (as you put it very well) 'sacrament'.
If the dog doesn't hunt (or doesn't hunt very well) you'll be right, no public moves to protect the murderers will be made.
I'm hoping, with some confidence, that these murdering women and ambulance chasing shysters just won't be able to resist the $$$ bait! (LOL)