Bring a large pot of salted water to a boil and cook the elbow macaroni until just al dente. Drain the pasta and set it aside while you prepare the rest of the dish.
In a bowl, combine the shredded chicken with the BBQ sauce, smoked paprika, and garlic powder. Toss until the chicken is evenly coated and set aside so the flavors can soak in.
Cook the bacon in a skillet over medium heat until crispy. Transfer it to a paper towel-lined plate and crumble once cooled. Reserve a small amount for topping later.
In a large pot, melt the butter over medium heat. Whisk in the flour and cook for about one minute to remove the raw flour taste while creating a smooth roux base.
Slowly pour in the milk and heavy cream while whisking continuously to prevent lumps. Allow the sauce to simmer gently until it thickens enough to coat the back of a spoon.
Reduce the heat and stir in the cheddar, mozzarella, and Monterey Jack cheese a little at a time until melted and creamy. Season with onion powder, garlic powder, smoked paprika, salt, and pepper.
Fold the cooked macaroni into the cheese sauce along with half of the BBQ chicken and half of the bacon. Stir gently until everything is evenly coated without breaking the pasta.
Transfer the mixture into a greased baking dish and top with the remaining BBQ chicken, bacon, and extra cheese. Bake at 375°F for about 15–20 minutes until bubbly and golden on top. Finish with a drizzle of BBQ sauce and sliced green onions before serving.