In a bowl, combine the papaya and lime juice. In a small saucepan, combine the sugar, pineapple juice, and orange juice and bring to a boil. Reduce the heat and simmer, stirring, until the sugar dissolves. Add the marinated papaya and simmer until tender, about 7 minutes. With a slotted spoon, transfer the papaya to a bowl and set aside.
In a small bowl, combine the cornstarch and water, stirring to dissolve. Add to the simmering juices and whisk. Add the lime and orange zests, and cook over low heat whisking until the mixture thickens, stirring occasionally. Remove from the heat and add the papaya. Add the butter and stir until melted. Let cool. Pour into the prebaked shell. Refrigerate until set, about 2 hours.
In a medium bowl, whip the cream and sugar until soft peaks form. Add the rum and whip until stiff peaks form, being careful not to overwhip. Top with whipped cream and sprinkle with the toasted coconut. Arrange the lime slices in a decorative pattern and serve. Refrigerate any leftover pie.
Yield: 1 (9-inch) pie