Add the peaches, pineapple and 1 cup of water to a blender and blend until completely pureed. Using a fine mesh sieve, pour puree through into a large bowl or measuring cup, using a spoon to press the last of the liquid out when you get to the end. Combine the juice with the remaining water, lime juice and simple syrup in a large pitcher. Taste and add more syrup if desired. Chill until cold. Before serving, add the frozen peach slices (to act as your ice cubes!) along with a few ice cubes if you’d like it super cold.