Preheat oven to 375°F Spray 2 (5 inch) square baking dishes or 2 (1.5 x 5.75 x 8 inch) foil pans with nonstick spray.
Mix zucchini, spinach, and mushrooms on microwavable plate. Cover and microwave on high until vegetables are crisp-tender, 3-4 minutes, stirring once after 2 minutes. Drain; stir in 1/8 tsp of salt.
Mix ricotta, 3 tbsp parmesan, oregano, red pepper flakes, and remaining 1/8 tsp salt in bowl. In each baking dish, layer, in order, 2 tbsp sauce, 1 half noodle, half of vegetables, 1 half noodle, half of ricotta mixture, 2 tbsp sauce, 1 half noodle, 1/4 cup sauce, and 1/2 tbsp parmesan. Cover with foil and bake 30 minutes. Uncover and bake until bubbling, 10-15 minutes.