In 2 separate non-reactive saucepans, place the mango in 1 and the papaya in the other. Add 1 cup of sugar and 2 1/2 cups of water to each pan. Place over medium heat and bring to a boil. Cook for 2 minutes. Remove from the heat and cool completely.
In a blender, puree the mango mixture until smooth. Remove and strain through a fine mesh strainer. Set aside. Wash out the cup of the blender and puree the papaya mixture until smooth. Remove and strain through a fine mesh sieve. In an ice cream maker, process each mixture, separately, according to manufacturer's directions.
Slice the strawberries and place in a mixing bowl. Add the remaining 1/2 cup of sugar and a splash orange liqueur, if using, and mix well. Cover and refrigerate for at least 30 minutes. To serve, lay some of the cubed angel food cake over the bottom each balloon wine glass or serving bowls. Place 2 small scoops of the mango sorbet over the cake. Spoon some of the berries over the top. Repeat with the remaining cake, papaya sorbet and berries. Garnish with a sprig of fresh mint.