1. Preheat broiler to high.
2. Combine first 6 ingredients in a medium bowl, stirring well to coat. Place juice in a small bowl. Peel, seed, and chop avocado. Add avocado to juice; toss. Add avocado mixture and tomatoes to tuna mixture; toss well to combine. Sprinkle cheese evenly over cut sides of bread, and broil for 3 minutes or until cheese is bubbly. Place 1 bread slice, cheese side up, on each of 4 plates, and divide tuna mixture evenly among bread slices.
Sustainable Choice: Solid white tuna is albacore, the most sustainable choice among varieties of tuna.