Preheat oven to 350°F.
Cut stems off chilies and scrape out seeds. Combine chilies, 6 tablespoons reserved soaking liquid and garlic in blender and puree until smooth.
Combine cream and chili puree in heavy large skillet. Bring to boil. Reduce heat; simmer 3 minutes. Whisk in lime juice. Season with salt. Strain sauce; return to skillet. (Sauce can be made 1 day ahead. Cover and chill.)
Melt butter in another heavy large skillet over medium heat. Add onion and mushrooms and sauté until onion is translucent and mushrooms are tender, about 5 minutes. Add cheese, cilantro, and tomatoes and 3 tablespoons cream sauce. Simmer until just heated through, about 4 minutes. Stir in avocado. Season filling with salt and pepper. Remove from heat.
Bring remaining cream sauce to simmer over low heat. Cook 1 tortilla in cream mixture until softened, turning to coat, about 15 seconds. Carefully transfer tortilla to baking sheet. Repeat with remaining tortillas. Cover remaining sauce and keep warm. Spoon generous 1/3 cup filling down center of each tortilla. Roll up tortillas, enclosing filling completely. Arrange seam side down. Cover enchiladas with remaining sauce and cheese, and cover with foil.
Bake enchiladas until heated through, about 20 minutes.