Place 2 ½ cups watermelon cubes in a blender; blend until liquefied. Transfer juice to a medium saucepan; stir in sugar and lime juice. Bring to a boil; reduce heat and simmer until sugar has dissolved, about 5 minutes. Set syrup aside to cool, about 20 minutes. Transfer syrup to a jar; cover. Chill in the refrigerator.
Meanwhile, place remaining 5 cups watermelon cubes on a cookie sheet lined with parchment paper; freeze until solid, about 4 hours.
Add frozen watermelon cubes, a few at a time, to the bowl of a food processor; pulse until puréed. Add ⅓ to ½ cup syrup, chamoy, and chile-lime seasoning to the food processor; pulse until smooth. Serve immediately or store in an airtight freezer-safe container in the freezer.