Simmer papaya in water with spices and sugar in a heavy medium saucepan, stirring until sugar has dissolved, until very tender, about 20 minutes. Stir in coconut milk, mint, and cilantro and simmer 15 minutes. Discard herbs and spice bundle. Purée soup in batches in a blender until very smooth (use caution when blending hot liquids; soup will be thick). If you have less than 4 cups, add water. Transfer to a shallow bowl and chill in freezer, stirring occasionally, until cold, 30 to 45 minutes. Whisk in lime juice, Tabasco, and salt. Season with lime juice and additional salt.