Soak the diced onions in cold water for 20 minutes to an hour. Drain. Toss together fruit, onion, chile, cilantro, and juice from one lime. Mix well and add salt to taste. It's best if this is let to sit for about an hour for the flavors to come together. Can be made up to one day in advance.
Heat a heavy-bottomed skillet. Fry carnitas over medium heat (adding a little oil if they begin to stick). Remove from pan. In the same pan, add 1/4 teaspoon of oil and add a tortilla topped with 1 ounce of cheese. Heat until cheese is just melted through. Top with a little meat and a heaping spoon of fruit salsa. Repeat with remaining tortillas. Serve with remaining limes, cut into wedges.