Prepare Shortcakes: Preheat oven to 400°. Whisk together flour and next 3 ingredients in a large bowl. Cut butter into flour mixture with a pastry blender until mixture resembles small peas.
Process toasted coconut in a food processor until finely chopped. Whisk together eggs, extracts, and 1 cup cream. Add egg mixture, chopped pecans, and toasted coconut to flour mixture, and stir with a wooden spoon just until blended. Knead dough in bowl about 10 times, using lightly floured hands. (Dough will be soft and moist.)
Turn dough out on a floured surface, and gently pat to a 1-inch thickness. Cut into 8 (2 1/2- to 3-inch) squares, reshaping dough once. Place shortcakes on a parchment paper-lined baking sheet, and chill 15 minutes. Press 1 pecan half into each shortcake; brush with remaining 1 Tbsp. cream. Sprinkle with sweetened flaked coconut.
Bake at 400° for 18 minutes or until golden brown. Cool on pan on a wire rack 20 minutes.
Meanwhile, prepare Strawberries: Stir together strawberries, lime juice, and 3 Tbsp. sugar.
Assemble: Split shortcakes in half horizontally. Place each shortcake bottom on a dessert plate, and top with about 1/3 cup strawberry mixture, desired amount of Sweet Mascarpone Cream, and shortcake tops.