Heat a large Dutch oven over high heat. Mix together the garlic powder, onion powder, paprika, salt and sugar in a small bowl. Place the pork pieces in a large bowl, then toss with the spices to coat. Add the oil to the Dutch oven and brown the pork in batches, about 5 minutes per side; remove to a plate. Place all of the pork back in the Dutch oven and cover with the onions and chicken broth. Bring to a boil, then cover and place in the oven. Cook until the pork is tender, about 2 1/2 hours.
For the BBQ sauce: Meanwhile, put the ketchup, vinegar, sugar, smoked paprika, Worcestershire and chile powder in a small pot and simmer for 5 minutes.
Remove the pork from the liquid and allow it to cool slightly. Cut off the pieces of fat and discard. Shred the meat with a fork.
For the nachos: Preheat the oven to 375 degrees F.
Place half of the chips in the bottom of a 12-inch cast-iron skillet. Layer on half the shredded pork, half the pepperoncini, half the red onion, half the bell pepper, half the pineapple, 1/4 cup BBQ sauce and half the cheese. Add a second layer, starting with the remaining chips and then the rest of the ingredients. Bake until the cheese is golden and bubbly, about 10 minutes.