Sort and wash beans; place in a Dutch oven. Cover with water to 2 inches above beans, and bring to a boil; cook 2 minutes. Remove from heat; cover and let stand 1 hour. Drain beans, and return to pan. Add 6 cups water, liquid smoke seasoning, and 2 bay leaves; bring to a boil. Cover, reduce heat, and simmer 45 minutes. Drain beans in a colander; discard bay leaves. Set beans aside.
Remove white papery skin of garlic heads, making sure not to peel or separate cloves. Wrap each head separately in aluminum foil. Bake at 350° for 1 hour; let cool for 10 minutes. Separate cloves, and squeeze to extract 1/3 cup pulp; discard skins. Set pulp aside.
Steam squash, covered, 6 minutes or until crisp-tender; set aside.
Combine onion and sherry in Dutch oven. Cover and cook over medium heat 10 minutes. Stir in vinegar and sugar. Cook, uncovered, over medium-high heat 15 minutes or until onion turns deep golden, stirring frequently. Add beans, garlic pulp, squash, broth, and next 7 ingredients; bring to a boil. Reduce heat; simmer 15 minutes. Remove from heat; discard bay leaf, and stir in tomato. Serve over Corn Risotto.