Cut pit and peel from mango and discard. Cut fruit into small pieces and put in a bowl.
Pit and peel avocado. Cut into small pieces and add to mango. Add lime juice, shrimp, chili, and green onions; mix gently.
Place tortillas side by side on a 14- by 17-inch baking sheet. Bake in a 400° oven until crisp and lightly browned, about 10 minutes (about 9 minutes in a convection oven), turning tortillas over once after 4 to 5 minutes. Let cool on pan 1 to 2 minutes.
Meanwhile, combine refried beans and broth in a microwave-safe bowl, cover, and heat in a microwave oven on full power (100%) until hot, about 1 minute.
Place tortillas on plates. Spread beans equally onto tortillas. Scatter lettuce equally over beans, then top lettuce with shrimp mixture and sour cream. Add salt to taste.