Chill 10-inch bread tin mold in freezer. Cut trimmed cakes in 1/2 to get 4 layers. Soak papaya with lime juice.
In large saucepan, heat together cold water, food coloring, sugar, 2 ounces rum and crystallized ginger for 10 minutes. Bring to a boil and stir in lime peel; cook 3 more minutes. Remove peel and discard. Add 2 tablespoons of this syrup to gelatin/rum mixture and mix well. Return all to pot, making sure gelatin is thoroughly dissolved. When mixture cools slightly, pour into chilled mold up to 1-inch deep. Place over bowl of crushed ice in freezer to set.
Remove mold from freezer and add another layer of jelly, tilting mold to coat evenly. Fit 1 cake layer, cut 1-inch smaller than mold, into mold then sprinkle with 1 tablespoon rum. Top cake layer with 1/3 of whipped cream, then add papaya, another cake layer, another tablespoon rum, sliced lime, then 1/3 more cream. Place strawberries, round side out, on top of gelatin around cake layer and place remaining berries on top of cream. Pour remaining gelatin along sides of mold over strawberries, then put on last cake layer and spread remaining cream on top. Chill in refrigerator for at least 4 hours or overnight.
To unmold: very carefully run a blunt edged knife around inside of mold. Dip mold in bowl of hot water for 6 seconds to loosen. Invert onto serving dish and garnish with extra whipping cream, if desired.