Heat oven to 425°F. Brush a large rimmed sheet pan with olive oil.
Toss shredded chicken with barbecue sauce, chili powder, garlic powder, cumin, and salt until coated.
Spread tortilla chips evenly on the pan, overlapping slightly to cover the surface.
Scatter sauced chicken, black beans, corn, and red onion over the chips. Sprinkle on half the cheese.
Bake until hot and the chips start to crisp, about 8 minutes.
Top with remaining cheese and bake 3–4 minutes more, until melted and bubbly.
Stir sour cream with lime juice and a splash of water to make a drizzle.
Finish with jalapeño, green onions, and cilantro. Drizzle lime crema and extra BBQ sauce if you like. Serve right away.