Have you tried approaching BBQ stores in the US to sell your product on consignment? It would be a lot cheaper to enter the US market that way instead of bearing all the cost of it on your own. You would also gain the confidence of the locals right away if you picked a reputable well known store.
It just so happens that these states became really good at BBQ, I dont think it really has to do with how close they are together. I should say that all of these states are known for different types of BBQ.
Kansas - They BBQ everything here, catfish, pork, beef, chicken, etc.
Texas- They mostly do beef here, brisket, short ribs, sausage, etc.
Carolinas- They do pork here, whole hog, pork butts, ribs, etc.
Tennesse- Im not familiar with this region.