In a medium saucepan, bring the cream and corn syrup to a boil. Put the bittersweet chocolate in a medium bowl and pour the hot cream over it. Let stand for 2 to 3 minutes, then whisk until smooth. Whisk in the butter. Refrigerate until firm, at least 1 hour.
Meanwhile, in a small dry skillet, toast the coconut over moderate heat, stirring constantly, until just lightly browned, about 2 minutes. Transfer to a small bowl and let cool. Stir in the cardamom, cloves, 2 tablespoons of the sugar and 1/4 teaspoon of the cinnamon. In another small bowl, whisk 1/3 cup of the sugar with the remaining 1 tablespoon of cinnamon, the allspice and the chipotle and ancho chile powders. In a third small bowl, whisk 1/4 cup of the cocoa powder with the five-spice powder and the remaining 1/3 cup of sugar. Put the remaining 1/4 cup of cocoa in another bowl.
Line a baking sheet with parchment paper. Scoop up level tablespoons of the ganache and drop them onto the parchment. Place the baking sheet in the refrigerator for 10 minutes. Using your hands, roll each mound of ganache into a ball; you may have to cool your hands in ice water periodically while you work.
Roll 1 truffle at a time into 1 of the coatings. Return the truffles to the baking sheet, cover loosely and refrigerate until chilled.