Finely chop mushrooms into coarse crumbs. Dice onion and bell peppers; mince garlic.
Heat oil in a wide skillet over medium-high. Cook mushrooms 6 to 8 minutes, until released liquid evaporates and brown spots appear.
Add onion and peppers; cook 5 minutes. Add garlic and tomato paste for 1 to 2 minutes, then stir in chili powder, cumin, paprika and oregano for 30 seconds.
Transfer skillet mixture to a 6-quart slow cooker. Stir in tomatoes, tomato sauce, broth, all three beans, soy sauce and salt.
Cover and cook on low 5 to 6 hours or high 2 1/2 to 3 1/2 hours, until vegetables are tender.
Mash about 1 cup beans into the chili. If needed, vent lid and cook on high 20 to 30 minutes; add broth if too thick.
Stir in frozen corn, cover and heat 5 to 10 minutes. Switch off cooker, add lime juice, taste and adjust salt.