I don't know why you're asking me this since I think conservatism is an outdated ideology that does not override the normal (IE: non-liberal) brain's tendency to trust people that look like them (or at least share an identity with). Conservatism works in a culturally cohesive society, something that never really described the United States to begin with. So what conservatives should have done is, first and foremost, stop being conservative. Being conservative in a significantly progressive population is like catching a cold while suffering from AIDS.
A better question is how should conservatives have responded to liberalism, since it's liberalism's machinations, both pre and post Jim Crow that did the actual damage. The answer of course is the Holy Trinity of good politics: Imperial rule, abolishment of the aristocracy and establishment of a minor Christian theocracy (pagan or Buddhist would probably work well too from a materialistic point of view).