Cook and stir ground beef and garlic in a large non-stick pot over medium-high heat until beef is no longer pink, about 10 minutes. Stir bell pepper, red onion, carrot, zucchini, and celery into beef mixture; cook and stir until vegetables soften, about 5 minutes.
Stir cumin, chili powder, oregano, coriander, and black pepper into beef mixture; cook for 1 minute. Stir tomatoes, corn, tomato soup, mushrooms, barbecue sauce, and taco seasoning into chili; bring to a boil. Reduce heat to low; cover and simmer, stirring occasionally, for 20 minutes.
Stir black beans, garbanzo beans, kidney beans, and baked beans into chili; simmer until heated through, about 15 minutes. Remove chili from heat; stir in cilantro and lime juice.