Trim ends off watermelon, then cut watermelon in half at an angle. Remove flesh from each half with a melon baller; set aside. Scrape out any excess flesh with a spoon for a clean, smooth interior.
Stand watermelon baskets upright on trimmed ends. Fill bottom third of each basket with about 40 watermelon balls. Place assorted melon and papaya slices on top of watermelon balls against the back of the basket, evenly dividing fruit between baskets. Fill in front with remaining watermelon balls. Sprinkle with lime zest. Serve with sea salt, sauce, and brittle as accompaniments.