Preheat the oven to 375 degrees F (190 degrees C). Spray a 3-quart baking dish with cooking spray.
Heat oil in a large saute pan over medium heat. Add eggplant, zucchini, tomatoes, bell pepper, onion, and garlic; cook, stirring occasionally until vegetables are tender, about 10 minutes. Sprinkle with Italian seasoning and salt; stir to combined.
Meanwhile, bring a large pot of lightly salted water to a boil. Add ziti and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Drain and rinse in cold water.
Mix spaghetti sauce and diced tomatoes together in a medium bowl.
Spread 1/3 of the sauce mixture in the bottom of the prepared casserole. Layer ingredients as follows: 1/2 of the ziti, 1/2 of the vegetable mixture, 1/2 of the Parmesan substitute, 1/2 of the mozzarella slices, 1/2 of the remaining sauce, all of the remaining ziti, all of the remaining vegetables, all of the remaining Parmesan substitute, and all of the remaining sauce. Set remaining mozzarella slices aside.
Cover loosely and bake in the preheated oven until bubbly, 25 to 30 minutes. Remove from the oven, uncover, and top with remaining mozzarella slices. Return to the oven and bake, uncovered, until cheese is melted and slightly browned, 10 to 15 minutes longer.