On a large baking sheet lined with parchment paper, place two of the tortillas side by side. Combine the two varieties of shredded cheese in a large bowl.
Take a third of the mixed cheeses and sprinkle it across the tortillas. Using ¼ c. of picante sauce for each tortilla, spoon the sauce over the shredded cheese. Take two more tortillas, place one on top of each stack. Take another third of mixed cheeses and sprinkle it across the tortillas, and top each with ¼ cup of picante sauce. Take the final two tortillas and place one on top of each stack. Place a medium baking sheet on top of the tortillas to press them down while baking. Place everything in the oven and bake for 10 minutes.
Remove the sheet from the oven, and remove the smaller baking sheet from the top. Add the cooked chicken evenly over the top of one of the tortilla-cheese stacks. Sprinkle half of the remaining cheese mixture over the chicken. On the other stack, evenly spoon the black beans across the top and add the last of the cheese over the beans. Sprinkle the cumin over both pizzas.
Switch the oven to the broiler setting. Place the baking sheet back in the oven and broil for 3-4 minutes until the cheese is melted and bubbling. Remove from the oven.
Top each tortilla pizza with diced tomatoes and shredded lettuce. Slice each pizza with a sharp knife into 4 wedges. Serve immediately with sour cream, salsa, or guacamole.