I will note from my perspective that drawing the South line between William & Mary and Wake Forest is a non-obvious choice.
In any event, I think I have still not seen an assessment on Rochester, which I think is very much not in the South. Rochester does have “brand” value, it is in a city but its main campus is sort of set apart (so more like Brown than Yale, say), and it very much fits the “mid size research university that has the feel of liberal arts” model.