Make the sauce: Combine the mayonnaise, parsley, scallions, hot sauce, Worcestershire sauce, and salt to taste in a bowl. Cover and refrigerate.
Slice the green tomatoes 1/4 inch thick and place in a large bowl. Combine the vinegar, sugar and 1 tablespoon salt in a saucepan. Put the pickling spice in a tea ball or tie in a square of cheesecloth with twine; add to the saucepan along with the dill. Simmer over medium heat, stirring, until the sugar dissolves, about 5 minutes. Add 2 cups cold water and pour over the green tomatoes. Let sit at room temperature 1 hour, 30 minutes.
Whisk the flour, cornmeal, chili powder and 1 teaspoon salt in a shallow dish. Whisk the eggs, 2 tablespoons water and 1 teaspoon salt in another shallow dish. Heat about 1 inch of peanut oil in a large skillet over medium heat until a deep-fry thermometer registers 375 degrees F.
Drain the green tomatoes and pat dry with a paper towel. Working in batches, dredge the green tomato slices in the flour mixture, then dip in the egg mixture and dredge again in the flour mixture. Fry in the hot oil, turning once, until the crust is golden, 3 to 4 minutes per side. Drain on paper towels and sprinkle with salt.
Spread each slice of bread with some of the sauce. Layer the fried green tomatoes and the yellow and red tomatoes evenly among 6 bread slices. Cover with the remaining bread slices.