Zest 1 lime and juice all 8 limes. Add peaches, honey, lime zest, lime juice to a blender and blend until smooth. Using a fine mesh strainer, press the puree through with a rubber spatula into a bowl. Discard any solids.
Add the rum to a large pitcher, smack each mint sprig before adding it to the pitcher (this helps to release the aromatics). Muddle the mint with a wooden spoon or muddler, stir in the peach puree to combine (can be made up to 1 day ahead).
At time of serving, stir in the soda water and serve over ice with an additional mint sprig for garnish.