Place pork shoulder in the crock of a slow cooker. Spread onion slices over the roast.
Combine chili powder, salt, garlic, chicken stock, and lime juice. Pour mixture over pork shoulder. Cook pork shoulder on low 6-8 hours or until shoulder is tender and pulls apart easily. Remove shoulder from crock and place in a large bowl . When cool enough to touch, shred meat.
Strain cooking liquid, discarding onions. Reserve 1/3 cup of cooking liquid. Mix reserved cooking liquid and barbeque cause. Stir into shredded meat. Set meat aside and keep warm.
In a large saucepan, melt butter over medium-high heat. Gradually whisk in flour. Cook for 2-3 minutes, stirring constantly. Do not allow the flour to brown. Slowly stir in milk, continuing to whisk until mixture is smooth and does not contain any lumps. Add the green chilis and bring the sauce to a boil. Continue to cook for about 5 minutes or until the sauce has thickened, stirring constantly. Remove from heat. Add the cheddar, salt, and cayenne pepper. Stir until sauce is smooth.
Preheat the oven to 400 degrees. Arrange tortilla chips in a thin layer in a 9 x 10 casserole dish or on a large baking sheet. Spread pulled pork evenly over chips, drizzle chili cheese sauce over pulled pork and top with half of the Monterey Jack cheese. Place in the oven and bake until cheese is melted, about 8-10 minutes.
Garnish nachos with sour cream, green onions, pickled jalapenos, black olives, and remaining cheese.