In a medium bowl, whisk together lime zest and juice, soy sauce, rice vinegar, ginger and honey. Slowly pour in vegetable oil, whisking until emulsified. Add watermelon and gently stir to coat. Refrigerate several hours or overnight.
Using a slotted spoon, remove watermelon from marinade. If desired, make a sauce by stirring 2 tablespoons of the leftover marinade into mayonnaise.
To serve: Divide rice among four bowls. Top with marinated watermelon, cucumber, radishes, edamame and avocados. Drizzle with mayonnaise sauce. Garnish with green onions and sesame seeds.