Soak the chiles in boiling water until softened, about 10 minutes. Drain and puree with the marjoram, oregano, garlic, one-quarter of the chopped onion and the pineapple juice in a blender until smooth. Add 1 1/2 teaspoons salt and 1/4 teaspoon pepper. Blend to combine.
Combine the pork and the marinade with a fork in a large bowl. Cover with plastic wrap and refrigerate for 30 minutes.
Preheat the broiler. Divide the pork mixture into 6 equal portions. Shape each portion into a 3/4-inch-thick patty. Lightly oil a rimmed baking sheet; place the patties on the baking sheet and broil until slightly charred and cooked through, about 9 minutes per side. Transfer the burgers to a plate and cover with foil to keep warm. Let rest about 8 minutes.
Meanwhile, lightly oil another rimmed baking sheet, add the pineapple and broil until slightly charred, about 2 minutes per side.
Spread about 1 teaspoon mayonnaise on the cut sides of each bun and broil them until the mayonnaise has melted, about 2 minutes. Place the burgers on the bottom halves of the buns. Top with the pineapple, cilantro, the remaining chopped onion and the bun tops.