Memphis Barbecue Nachos

1 pound smoked pork shoulder, barbecued pork or smoked chicken, chopped
1 (16-ounce) jar spicy nacho cheese sauce
1 pound round tortilla chips
1 (18-ounce) bottle Memphis-style barbeque sauce, see Cook’s Note*
Dry barbecue spice rub or chili powder, as needed
1 small (6 to 8-ounce) can sliced jalapenos, drained
In separate saucepans over low heat, warm the pork and spicy nacho cheese sauce. Divide the chips among 4 shallow bowls. Top the chips with barbecue pork. Layer some cheese sauce over the pork. Top the cheese sauce with barbecue sauce. Sprinkle each bowl with dry rub barbecue seasoning and jalapenos to taste.