Preheat oven to 350°F with rack about 7 inches from the heat source (middle position). Combine zucchini slices, ½ teaspoon crushed red pepper and ¼ teaspoon salt in a medium bowl; toss until well coated. Let stand at room temperature.
Heat 1 tablespoon oil in a 12-inch oven-safe skillet over medium-high heat. Add 1 pound ground beef; cook, breaking the meat into bite-size pieces, until mostly browned, about 3 minutes. Stir in chopped onion, chopped bell pepper, sliced garlic and 1 teaspoon Italian seasoning; cook, stirring often, until the onion softens, about 2 minutes.
Stir in 1½ cups marinara, 1 tablespoon vinegar and the remaining 1 teaspoon Italian seasoning; cook, stirring occasionally, until gently simmering, about 2 minutes. Remove from heat and carefully transfer half of the meat sauce (about 2 cups) to a medium heatproof bowl. Spread the remaining meat sauce (about 2 cups) in an even layer in the skillet. Layer half of the zucchini slices (about 2 cups) over the meat sauce. Spread the remaining meat sauce over the zucchini. Top with the remaining zucchini slices.
Sprinkle with ½ cup Cheddar and ¼ cup Italian cheese. Bake until the cheese is melted and the zucchini is tender, about 30 minutes. Increase oven temperature to broil. Broil until the cheese is browned, about 2 minutes. Sprinkle with 1 tablespoon basil.
