1. Combine rind, 3 tablespoons juice, and next 5 ingredients (through black pepper) in a large bowl, stirring well with a whisk. Reserve 1 1/2 tablespoons juice mixture. Add remaining 2 tablespoons juice, corn, and next 4 ingredients (through crab) to remaining juice mixture; toss gently to coat.
2. Arrange 2 tomato slices and 1/2 cup cherry tomatoes on each of 4 plates. Drizzle about 1 teaspoon reserved juice mixture over each serving. Top each serving with 1 cup corn and crab mixture.