Have tried Blak now. It tastes like that someone took that pot of coffee that's been sitting in the break room since morning -- you know, the dregs of it -- chilled it, and mixed it half-and-half with the Coke that's half real syrup and half artificial sweetener, and then ran it through the carbonation process again just to make sure that it really was fizzy enough. Judging from the ingredients list, that's about exactly what they did.
I have a Cunning Plan to attempt to duplicate or better the recipe when we're out tonight. This depends on a glass of Coke, an empty glass with plenty of ice, and a pot of coffee. Oh, and all the sugar packets on the table.