I guess Kentucky really is Yankee. Lexington KY has honest to corned beef delis. Actually Google shows that they are spotted, rarely, even in Mississippi. Usually they masquerade as such things as co-ops and Jimmy John Sandwich Shoppe. But you need Google (or Bing) to ferret them out. The Yellow Pages just won't do.
You don’t need no silly Deli sandwich in Arkansas, Mississippi, or Louisiana. Just take a trip to the local restaurant and order a shrimp po-boy. After eating that little bit of pure culinary joy, you will be hooked and probably never want to leave the South.
Alternatively, go to Central Grocery in New Orleans (French Quarter) and order a Muffaletta. But, fair warning, after eating this, you may never be able to go into a Yankee deli again.