Make the crust: Pulse the flour, coconut, 2 tablespoons butter, the shortening and salt in a food processor until it looks like fine meal. Add the remaining 4 tablespoons butter and pulse until it is in pea-size pieces. Drizzle in 2 tablespoons cold water and pulse until the dough just comes together. Turn out onto a piece of plastic wrap; use the plastic to help form the dough into a disk. Wrap tightly and refrigerate until firm, at least 1 hour or overnight. (The dough can be frozen for up to 2 months; thaw at room temperature.)
Roll out the dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch pie plate, fold the overhanging dough under itself and crimp the edge with your fingers. Chill at least 30 minutes.
Preheat the oven to 350 degrees F. Line the crust with foil and fill with pie weights or dried beans. Bake until golden around the edge, about 20 minutes. Remove the foil and weights and continue baking 5 more minutes. Transfer to a rack and let cool completely.
Meanwhile, make the filling: Reduce the oven temperature to 325 degrees F. Gently whisk the pumpkin, coconut milk, sugar, eggs, rum, vanilla, cinnamon and allspice in a large bowl until combined. Pour into the prepared crust and place on a rimmed baking sheet. Transfer to the oven and bake 1 hour. Sprinkle more coconut around the edge of the pie; continue baking until the center is almost set but still jiggles slightly, about 15 more minutes. Transfer to a rack to cool completely.