Working in two batches if necessary, cook bacon in a large skillet over medium heat until brown and crisp, 6 to 8 minutes per side; transfer to a paper-towel-lined plate to drain. Pour off all but 2 tablespoons rendered fat from skillet.
Season turkey generously with salt and pepper. Add to skillet, and cook over medium heat until opaque throughout, 2 to 3 minutes per side; transfer to a paper-towel-lined plate to drain.
In a small bowl, mash avocado, lime juice, and chiles with a fork; season with salt and pepper.
Spread avocado mixture on one side of each slice of toast. Layer turkey, bacon, tomato, and toast to form four triple-decker sandwiches. To serve, skewer with toothpicks; slice in half with a serrated knife.
Chicken cutlets are a good substitute for the turkey. You can even use sliced cooked turkey or chicken from the deli counter; in that case, skip step 2. After halving avocado and removing the pit, slide a large spoon between skin and flesh to remove peel in one piece.