Bring water and sugar to a boil. Add peaches. Reduce heat, and simmer until tender, 5 to 7 minutes. Using a slotted spoon, transfer peaches to a plate, reserving syrup. Let peaches cool; peel, and pit. Stir together syrup, light rum, sweet red vermouth, fresh lemon juice, and bitters. Place half a peach in each of 6 saucer Champagne glasses. Fill with crushed ice, and top with punch.
This drink is traditionally made with canned peaches and syrup. But poaching fresh peaches yields a richer, more intense flavor.