Puree and strain peaches and their liquid (you should have 3 1/3 cups puree). Place in a medium saucepan over medium-high heat, and bring to a simmer. Let simmer about 8 minutes, until reduced to 2 cups. Bring sugar and 1/4 cup water to a boil in a small saucepan and cook until the sugar is completely dissolved, about 1 minute. Combine with reduced peach puree and let cool. Stir in lime juice and rum; refrigerate syrup, covered, until cold. For each daiquiri, pour 2 tablespoons syrup over 1/2 cup crushed ice.