Beat together the cheeses in a large bowl with a hand mixer on medium speed until smooth. Add the granulated sugar, rum and brown sugar and continue beating on medium speed until combined. Fold in 1 cup of the coconut, the pecans, melted chocolate and vanilla.
Spray a 9-inch springform pan with nonstick cooking spray and then line it with ladyfingers . Alternate layers of the chocolate mixture with the remaining ladyfingers, using an offset spatula or butter knife sprayed with nonstick cooking spray. Chill overnight.
Remove from the pan and decorate with whipped cream . Sprinkle the remaining 1/2 cup coconut over the whipped cream and lightly grate chocolate over the top to decorate.