Line bottom of a 13 x 9-inch baking pan with wax paper; set aside.
To prepare cake, lightly spoon the flour into a dry measuring cup, and level with a knife. Combine the flour and 6 tablespoons sugar, stirring with a whisk.
Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and salt; beat until soft peaks form. Add 6 tablespoons sugar, 2 tablespoons at a time, beating until stiff peaks form. Beat in 3/4 teaspoon juice and extracts.
Sift 1/4 cup flour mixture over egg white mixture; fold in. Repeat with remaining flour mixture, 1/4 cup at a time. Gently spread batter into prepared pan; sprinkle with almonds. Bake at 325° for 25 minutes or until cake springs back when lightly touched.
Place a clean dishtowel over a large wire rack; dust towel with powdered sugar. Loosen cake from sides of pan; turn out onto dishtowel. Carefully peel off wax paper. Lightly coat another large wire rack with cooking spray; place over cake. Invert cake; remove first rack and towel. Cool completely.
To prepare sauce, combine 2 tablespoons granulated sugar, 2 tablespoons brandy, 2 teaspoons juice, and raspberries in a food processor. Process until well blended. Press mixture through a sieve into a bowl, reserving 3/4 cup. Discard solids.
To prepare fruit, combine blackberries, blueberries, 3 tablespoons granulated sugar, and 2 tablespoons brandy. Let stand 1 hour.
To prepare glaze, combine jam and water in a 1-cup glass measure. Microwave at high 30 seconds or until jam melts, stirring once.
Cut the cake into 12 rectangles using a serrated knife. Place 1 cake rectangle on each of 6 dessert plates. Drizzle each serving with 2 teaspoons glaze; top each serving with 1/2 cup fruit mixture and 1 cake rectangle. Drizzle 2 tablespoons of the sauce around each shortcake.