Hey Pete,
Brown Turkey (in my opinion) is nto a good fig to sell at market. They need to be "beyond" dead-ripe (squishy, mushy) to have any character of flavor. Anything less and all you're going to get is sweet and possibly watery flavor like eating a watermelon rind instead of the watermelon. Some people may actually react poorly to the sap content of the skin (throat constriction, etc.)
My Brown Turkey figs just finished ripening their breba crop about 3 weeks ago. With you in NC, you probably purchased breba figs, not main crop figs. The brebas are generally worthless on my 5-year-old in-ground BT tree. Doesn't get much worse!
Whole Foods (more like "Whole Paycheck") had hordes of BT figs last fall around Oct/Nov. Same issue: whoever picked them chose to pick about a week prior to being semi-ripe, so they were firm. My neighbor bought a four-pack. Flavorless, firm thick skin, hardly juicy inside, no figgy flavor, very sweet.
Not my schtick.