To make Special Tomato mixture, combine tomatoes, minced chilli, salt, and pepper in heavy small saucepan over medium heat. Cook 10 minutes, stirring occasionally.
Stir both meats, onion and garlic in heavy large saucepan over medium heat until meat is no longer pink. Mix in beer or water, then all remaining ingredients except masa. Mix in Special Tomato mixture. Cover and simmer until chili is reduced to 12 cups, stirring occasionally, about 3 hours.
Degrease chili. Stir dissolved masa into chili. Cover and simmer 30 minutes. Refrigerate overnight to blend flavors. (Can be prepared 5 days ahead.)