Strawberry Daiquiri Slush with Honeydew Melon

1 (12-oz) package frozen unsweetened strawberries
1/3 cup light corn syrup
1/4 to 1/3 cup white rum
2 tablespoons fresh lime juice
1/2 ripe honeydew melon, seeded and flesh cut into 1/2-inch cubes

Garnish: lime slices

Purée frozen berries, corn syrup, rum to taste, and lime juice in a blender until slushy. Spoon into 6 (8-ounce) wineglasses or other stemmed shallow glasses and top with melon.