Trim and discard excess fat from pork. Cut pork into 1/2-inch cubes.
In a 5- to 6-quart pan, combine pork, onion, garlic, cumin seed, and 1/2 cup broth. Cover, bring to a boil over high heat, and cook 10 minutes. Then boil, uncovered, stirring often as liquid evaporates and a brown film forms on pan bottom, 5 to 12 minutes. Add another 1/2 cup broth, stir browned bits free, and stir often until liquid evaporates again, 3 to 6 minutes. Add 1 can red chili sauce and stir browned bits free, then reduce the heat to simmering and cover.
Meanwhile, remove seeds and veins from chilies, then rinse and finely chop.
Add corn and red bell pepper to pork. Then stir in chilies to taste. Simmer until meat is tender enough to pull apart, about 1 1/4 hours total; stir often. Remove from heat and mix in chopped cilantro. Add salt to taste.
Pour remaining red chili sauce into a rimmed pan (at least 10 in. wide). Dip 1 tortilla in sauce, turning to coat each side, and lay in a round casserole or ovenproof platter, 12 to 14 inches wide. Cover tortilla with about 1/7 (about 1 cup) of the pork sauce. Sprinkle with 1/4 cup Mexican cheese blend and 2 tablespoons cotija cheese. Repeat steps, ending with a tortilla on top. If making up to 1 day ahead, cover and chill pie, remaining chili sauce, and the cheeses separately.
Bake tortilla pie, covered, in a 350° oven for 25 minutes (1 hour if chilled). Uncover and continue to bake until hot in center (140° on a thermometer), about 20 minutes. Sprinkle with the remaining Mexican cheese blend and bake until it melts, about 5 minutes longer.
Meanwhile, peel, pit, and slice avocado. Also heat remaining chili sauce. Drizzle about 1/4 cup of the sauce over the tortilla pie. Garnish with avocado slices, remaining cotija cheese, and cilantro sprigs. Cut into wedges. Offer remaining chili sauce to spoon onto portions to taste.