In a small saucepan, combine the first 5 ingredients. Bring to a boil. Reduce heat; simmer, uncovered, 5-6 minutes or until slightly thickened. Strain; discard peels. Add juices to the syrup; cool slightly.
Place half of the juice mixture and 2 cups strawberries in a blender; cover and pulse until nearly smooth. Pour into a 2-qt. freezer container. Repeat with remaining juice mixture and berries.
Cover and freeze 12 hours or overnight, stirring several times. Ice may be frozen for up to 3 months. Just before serving, break apart with a large spoon.