Combine first 4 ingredients; stir well with a whisk.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high heat. Place mushrooms in a single layer in pan; sauté 3 to 4 minutes on each side or until liquid is almost absorbed. Remove from pan and place in a large bowl. Cover and keep warm.
Add 1 teaspoon oil to pan and place over medium heat. Cut zucchini slices in half crosswise. Place half of zucchini slices in pan; sauté 7 to 9 minutes or until zucchini is lightly browned. Repeat with remaining zucchini and 1 teaspoon oil. Remove from heat and place in bowl with mushrooms. Drizzle with red wine vinegar mixture and remaining 1 teaspoon oil; toss gently.
Cut baguette crosswise into 4 pieces; cut each piece in half lengthwise. Place slices on a baking sheet, cut sides up, and broil 1 minute or until toasted.
Combine goat cheese and thyme; spread evenly over toasted baguette slices. Layer 4 toast slices evenly with 1/4 of mushroom mixture and tomato slices. Top with remaining baguette slices.