Preheat the oven to 350 degrees F. Prick the sweet potatoes all over with a fork and place on a rimmed baking sheet; bake until tender, about 45 minutes. Let cool, then peel off the skins and puree the flesh in a food processor until smooth. (You?ll need 2 cups sweet potato puree.)
Gently roll out the pie dough into a 12-inch round on a lightly floured surface. Ease into a 91/2-inch deep-dish pie dish; fold the overhanging dough under itself and crimp the edges. Line the crust with foil and fill with dried beans or pie weights. Bake until the crust is just golden around the edges, about 15 minutes. Remove the foil and beans and continue to bake until the crust is golden on the bottom, about 15 more minutes. Let cool.
Combine the sweet potato puree, 1/2 cup granulated sugar, the brown sugar, melted butter, 3 tablespoons rum, the vanilla, cinnamon, ginger, salt and eggs in a large bowl. Beat with a hand mixer until combined. Add the coconut milk and continue to mix. Pour the filling into the pie crust and bake until the filling is set, 1 hour 15 minutes to 1 hour 25 minutes. (Cover the crust with foil if it gets too dark.) Place the pie on a rack and let cool, about 2 hours.
Pour the heavy cream into a bowl and beat with the mixer until thickened. Add the remaining 3 tablespoons granulated sugar, the remaining 1 tablespoon rum and the orange zest. Whip until stiff peaks form. Serve the pie topped with the whipped cream.