Preheat the oven to 375 degrees. Toss the meat with 1 cup of BBQ sauce and set aside.
Coarsely mash the beans in a bowl with the lime juice, about half the Cajun Rub, and salt to taste. In another bowl, toss the tomatoes with the jalapenos and the 1/2 cup cilantro. Season with additional salt and pepper to taste.
Scatter half the chips in a baking dish. Scatter the meat, beans, and 1/3 cup sour cream, and about half the tomato mixture over the chips. Cover with remaining chips, then scatter the remaining tomatoes, sauce, and Cajun Rub evenly over the chips. Sprinkle the shredded cheese over all.
Bake the nachos until cheese melts and begin to brown (about 7 minutes). Serve warm, garnished with additional sour cream and cilantro.