Marinate and cook pork: Combine juice, garlic, cumin, and 1 teaspoon salt in a large bowl, then whisk in oil. Add pork and toss to coat, then marinate, covered and chilled, turning occasionally, 3 hours.
Drain pork, reserving marinade, then put pork in pressure cooker and add enough water to cover. Seal pressure cooker with lid and cook at high pressure, according to manufacturer's instructions, 30 minutes. Remove from heat and let pressure fall naturally.
Make filling: When pork is cool enough to handle, drain, discarding liquid, and coarsely shred. Heat 2 tablespoons oil in a deep 12-inch heavy skillet over medium-high heat until it shimmers, then lightly brown pork, stirring, until crisp.
Transfer pork to a bowl with a slotted spoon, then add chorizo and ham to skillet and cook, stirring frequently, until slightly crisp, about 5 minutes. (If chorizo is very lean, add 1 tablespoon oil.) Add onions and bell peppers and cook over medium heat, stirring frequently, until tender but not browned, about 15 minutes. Add paprika and cook, stirring, 1 minute.
Return pork to skillet, then add tomatoes with their juice, tomato paste, Sherry, and reserved marinade. Simmer, covered, stirring occasionally, until slightly thickened, about 20 minutes. Remove from heat and keep warm, covered. Prepare crust and bake pie: Preheat oven to 400°F with rack in middle. Oil a 13- by 9-inch glass baking dish.
Bring broth and 1 cup hot water to a boil in a small saucepan, then remove from heat and cover.
Combine baking powder and 1/2 teaspoon salt in a large bowl. Whisk in oil until smooth, then stir in cornmeal. Stir in hot broth and let stand, uncovered, 10 minutes.
Stir eggs into cornmeal mixture. Set aside 1 1/2 cups batter (for top crust).
Stir corn kernels into remaining batter (for bottom crust) and spread over bottom and up sides of baking dish. Spoon filling into crust and sprinkle with cheese.
Stir remaining 1/4 cup hot water into reserved batter and spread over top. Bake until top is browned, about 40 minutes. Let stand 15 minutes before slicing.