In the container of a blender, combine watermelon, ½ cup plus 2 tablespoons sugar, 2 tablespoons lemon juice, and 1 tablespoon corn syrup. Blend on high speed until completely smooth. Strain mixture through a fine-mesh sieve into a medium bowl, pressing solids to extract as much liquid as possible. Discard solids, and set watermelon liquid aside. Repeat blending and straining procedure with cantaloupe, remaining ½ cup plus 2 tablespoons sugar, remaining 2 tablespoons lemon juice, and remaining 1 tablespoon corn syrup.
Fill 10 (3-ounce) plastic ice pop molds halfway with cantaloupe mixture. Freeze until firm, approximately 1 hour. Fill molds with watermelon mixture, and freeze until solid, approximately 4 hours.