Combine syrup and 3 tablespoons rum in a small bowl. Brush ladyfingers with syrup mixture, and dip into crumbs, coating both sides. Line sides and bottom of a 9-inch ungreased Springform pan with prepared ladyfingers; set aside.
Combine gelatin, milk, rum, egg yolks, and 1/3 cup brown sugar in a medium saucepan; cook over low heat, 5 to 10 minutes, until thickened. Remove from heat, add pumpkin, orange rind, and pumpkin pie spice; stir well. Add 1/3 cup brown sugar; beat well.
Beat egg whites (at room temperature) in a large bowl, until stiff peaks form. Gently fold pumpkin mixture and whipped cream into egg whites. Fold in almonds. Pour mixture into prepared pan.
Cover, and chill at least 6 hours or overnight. Pipe rosettes of Rum Cream on top of charlotte, and sprinkle with Sugar Almonds to garnish.