Have Carter win in 1980 (perhaps because a regime change in late October in Iran leads to the hostages being freed), then when the economy recovers and the 1984 election happens, the next Democratic candidate is a Southerner as well, or at least has a Southern running mate, leading to an election map not unlike '76 again. After there are enough Southern Democratic candidates, the Democrats will have changed their views in such a way as to gain Southern support.