Dem reps from majority white non-hispanic areas include Graham, Cooper, Murphy, probably Frankel and Kastor, and possibly a few others from Florida. So basically in the deep south, Barrow was the last one, though I suppose you could call FL-02 the deep south.
And Price, Beyer, and Connolly. None of those are particularly culturally southern, but at least Price (NC-4, where I live) is surrounded by the South. South Fla. and No. Va. aren't totally in the cultural South, so that leaves Price, Cooper, and Graham.
BTW, where is the census (or other) link for CD data?