Add the chilled watermelon cubes to a blender and puree until completely smooth, about 30 seconds. Strain through a fine-mesh sieve into a bowl to remove any pulp, pressing gently with a spatula.
In a small saucepan over medium heat, combine the sugar and 1/4 cup of the watermelon juice. Stir until the sugar dissolves completely, about 2 minutes. Remove from heat and let cool to room temperature.
In a large mixing bowl, whisk together the remaining watermelon juice, cooled sugar syrup, heavy cream, lime juice, lime zest, and corn syrup until evenly combined. Taste and adjust lime juice if needed.
Pour the mixture into a shallow 9x13-inch metal baking pan. Place in the freezer on a flat surface.
After 45 minutes, remove the pan and use a fork to scrape and stir the frozen edges into the center. Repeat this process every 45 minutes for 3 hours total, breaking up ice crystals each time.
Once the mixture is uniformly frozen but still slightly soft, transfer it to an airtight freezer container. Press plastic wrap directly onto the surface, seal, and freeze for at least 1 more hour before serving.
Let the ice cream sit at room temperature for 5-10 minutes before scooping. Use a sturdy ice cream scoop dipped in warm water for clean, round scoops.
