Cut zucchini into strips 1/4 inch thick. Heat oil; add garlic and onion and cook until vegetables are tender but not browned. Add meat and brown, stirring to keep meat crumbly. Add tomatoes, tomato paste, mushrooms, wine, oregano, thyme, basil and salt and pepper to taste. Simmer uncovered 1-1/2 hours. Place half of the zucchini strips in an oiled shallow casserole. Top with half of the Mozzarella and Ricotta cheeses. Add half the meat sauce. Repeat layers. Top with Parmesan cheese. Bake at 350 degrees for 40 minutes.