Preheat oven to 450°F with racks in upper and lower thirds
Cook rice according to package instructions
While rice cooks, toss zucchini with 1 tablespoon oil and 1/2 teaspoon salt in a shallow baking pan
Toss tomatoes with 1/2 tablespoon oil and 1/4 teaspoon salt in another baking pan
Roast zucchini in upper third of oven and tomatoes in lower third, turning vegetables once halfway through roasting, until tender and light golden, about 10 minutes for tomatoes; 20 minutes for zucchini
Leave oven on
Meanwhile, cook onion and garlic with 1/2 teaspoon salt in 2 tablespoons oil in a large heavy skillet, covered, over low heat, stirring occasionally, until very tender, 15 to 20 minutes
Stir together onion mixture, cooked rice, eggs, thyme, 1/4 cup cheese, 1 tablespoon oil, 1/4 teaspoon salt, and 1/2 teaspoon pepper
Spread half of rice mixture in a shallow 2-quart baking dish, then top with half of zucchini
Spread remaining rice mixture over zucchini, then top with remaining zucchini
Top with tomatoes and drizzle with remaining 2 tablespoons oil, then sprinkle with remaining 1/4 cup cheese
Bake in upper third of oven until set and golden brown, about 20 minutes