Those "double digit traditional conservatives" you point out have traditionally gone by another name: Libertarian. We all know how successful they have been in convincing the country about the validity of their GOP fiscal + Dem social point of view.
The beauty of Ronald Reagan is he could talk a good game about abortion, immigration, and the general culture war but in fact he didn't give two hoots in hell about it. He was a traditionalist conservative who was deeply committed to a strong defense, free trade, and law and order and a sound economy. Reagan sounded like a culture warrior but he wasn't. And that was his genius....