Spend a few minutes reading up on what happened to the Whigs in the 1850s and the answer becomes fairly clear.
The Whigs couldn't agree on slavery (which, but for the slaughter of 50 million babies, would be the most critical social issue in American history), so the anti-slavery social conservatives left and formed the GOP. Within a few years the Whigs had disappeared and the GOP became the dominant party for decades.
I agree. Social conservatives should seriously consider leaving the GOP.
I think your analysis is spot on. A couple things are different though. The 2 dominant political parties have been able to structure election laws in such a way that it gives them a near monopoly. The media only pays attention to a 3rd party when it will benefit the Rats. On the basis of these two factors alone it is easier to push back the "mushy" moderates and take control of the party than to leave and start over.
I think the key to gaining control and keeping it is to control the money. All too often we elect conservatives who then abandon us once they are in power. I think that's because they want to get reelected and the party controls the money. Also, we need aggressive young conservative turks to run the party organization that is responsible for finding candidates.
Finally, on the issue of abortion (the slaughter of innocent life) we need to keep pushing, but change our tactics. IOW, appeal to the concern over the safety of the mother. Abortion clinics should be better regulated, only doctors allowed to perform them, their business structure should be transparent and who their lobbyists are should be publicized.