Combine first 5 ingredients in a large bowl; cover and chill.
Carefully remove 6 (2-inch) strips of rind from limes using a vegetable peeler, making sure to avoid the white pithy part of the rind. Combine lime strips, water, sugar, and 6 mint sprigs in a small saucepan; bring to a boil. Cook until reduced to 1/2 cup (about 5 minutes). Discard lime strips and mint sprigs; cool. Stir in chopped mint, juice, and grated rind. Pour over fruit, tossing gently to coat. Garnish with additional mint sprigs, if desired.