Post-1968 I don't think that a three-party equilibrium of Republicans in the South, Democrats in the Northeast and West Coast, and Libertarians in the Midwest is too unrealistic.
Pre-1968, another might turn to Democrats and Republicans, and then States' Rights in the South, if Strom Thurmond's 1948 run started a genuine political party, sticking around and so on. I imagine George Wallace's 1968 run would've been under that banner instead.