1. Combine sugar and water, stirring until sugar dissolves.
2. Puree sugar mixture and remaining ingredients, in 2 batches, in a blender until smooth.
3. Press fruit mixture through a fine sieve into a large bowl using a spatula or the back of a wooden spoon.
4. Pour mixture into freezer container of an ice cream maker; freeze according to manufacturer's instructions (about 30 minutes). Transfer to an airtight container, and freeze at least 3 hours or up to 1 week. Let stand in the refrigerator 30 minutes before serving.