I would try the markets in areas that are mixed-ethnic, such as the ones on Villa . . . or, is Chan's on Lincoln still open? I've been out of state since '98 but I used to visit Chan's for Louisiana and other Southern-type ingredients.
Chicken & dumplings sounds wonderful. Another idea, which I read a few years back, is to stew up a regular-type bird until the meat is practically leached of all flavor, then strain the stock and cook another chicken in it, and use that meat in the finished dish.