Carter's 1976 coalition didn't actually have much to do with the way any pre-1964 Democrat won the South.
really? I'm pretty sure he got at least 40% of the white vote in every southern state.
Carter 1976 got between 40% and 55% of the white vote in the Southern states.
Wilson 1916, who had the same national margin of Carter 1976, had ~85% of the votes in the Deep South. Only white people could vote, so, he had ~85% of the white vote of the Deep South. But Wilson 1916 and Carter 1976 margins in Tennessee and Kentucky were very similar.
The map of 1976 looks like old maps, but not the percentage of the vote of the ethnic groups.
The map of 1976 looks like also the map of 1960, not only the map of the states, but also the map of the counties. In both 1960 and 1976, D won the rural south and the urban north, and lost the west. The only difference is that the map of 1960 is more similar to the recent maps than the map of 1976 is.