Place eggplant slices in a colander. Sprinkle evenly with 1/2 teaspoon salt; toss well. Let stand 10 minutes. Rinse slices thoroughly; dry with paper towels.
Combine vinegar, wine, and sugar in a small saucepan over medium heat; bring to a boil. Reduce heat, and simmer until reduced to 1/4 cup (about 8 minutes).
Trim ends from the zucchini and yellow squash; slice each lengthwise into 4 (1/4-inch-thick) slices. Flatten pepper pieces with hand. Brush eggplant, zucchini, squash, and pepper pieces with oil; sprinkle with remaining 1/4 teaspoon salt and black pepper. Place pepper pieces, skin side down, eggplant, zucchini, and squash on a grill rack; grill 8 minutes or until tender, turning once.
Combine cheese, basil, and oregano.
To assemble stack, place 1 eggplant slice on a plate; top with one-fourth of cheese mixture. Lay one strip of yellow squash and one strip of zucchini side by side. Drizzle with 1 1/2 teaspoons balsamic mixture. Top with one pepper piece. Top with one eggplant slice and drizzle with 1 1/2 teaspoons balsamic mixture. Repeat procedure three times with remaining eggplant, cheese, squash, zucchini, peppers, and balsamic mixture. Let stand 5 minutes before serving.