I'm very late to this party, but found the thread looking for a cheeseshop in the District after the closing of Cowgirl Creamery and a disappointment at Cork Market (it's fine, just not what I wanted it to be).
Southern caviar is the delicious black-eye pea salad. Pimento cheese is "Southern pate".
Following my grandmother, and more high end Southern places than you'd expect, I use Duke's and actually prefer it to homemade mayo in mine. Unlike my grandmother, I find that a shot of rye and a handful of pickled piquillo peppers are a game changer.
On the store front, Cheestique looks like my place. They have my go-to cheeses (Beecher's Flagship, Sweet Grass Green Hill, Lamb Chopper). I'd rather not cross the river, and remain happy to hear suggestions, particularly those that are easy by public transit.