Put oven rack in middle position and preheat oven to 350°F. Butter a 13- by 9-inch baking pan and line bottom with wax paper, leaving a 2-inch overhang on 2 ends, then butter paper.
Beat whites in mixer fitted with whisk attachment at medium-high speed until they just hold stiff peaks. Add 1/4 cup sugar a little at a time, beating at high speed until whites hold stiff, slightly glossy peaks. Transfer to another bowl.
Switch to paddle attachment, then beat together almond paste and remaining 3/4 cup sugar until well blended, about 3 minutes. Add butter and beat until pale and fluffy, about 3 minutes. Add yolks and almond extract and beat until combined well, about 2 minutes. Reduce speed to low, then add flour and salt and mix until just combined.
Fold half of egg white mixture into almond mixture to lighten, then fold in remaining whites gently but thoroughly.
Divide batter among 3 bowls. Stir red food coloring into one and green food coloring into another, leaving the third batch plain. Set white batter aside. Chill green batter, covered. Pour red batter into prepared pan and spread evenly with offset spatula (layer will be about 1/4 inch thick).
Bake red layer 8 to 10 minutes, until just set. (It is important to undercook.)
Using paper overhang, transfer layer to a rack to cool, about 15 minutes. Clean pan, then line with wax paper and butter paper in same manner as above. Bake white layer in prepared pan until just set. As white layer bakes, bring green batter to room temperature. Transfer white layer to a rack. Prepare pan as above, then bake green layer in same manner as before. Transfer to a rack to cool.
When all layers are cool, invert green onto a wax-paper-lined large baking sheet. Discard paper from layer and spread with half of preserves. Invert white on top of green layer, discarding paper. Spread with remaining preserves. Invert red layer on top of white layer and discard wax paper.
Cover with plastic wrap and weight with a large baking pan. Chill at least 8 hours.
Remove weight and plastic wrap. Bring layers to room temperature. Melt chocolate in a double boiler or a metal bowl set over a saucepan of barely simmering water, stirring until smooth. Remove from heat. Keep chocolate over water.
Trim edges of assembled layers with a long serrated knife. Quickly spread half of chocolate in a thin layer on top of cake. Chill, uncovered, until chocolate is firm, about 15 minutes. Cover with another sheet of wax paper and place another baking sheet on top, then invert cake onto sheet and remove paper. Quickly spread with remaining chocolate. Chill until firm, about 30 minutes.
Cut lengthwise into 4 strips. Cut strips crosswise into 3/4-inch-wide cookies.
Cookies keep, layered between sheets of wax paper or parchment, in an airtight container at room temperature 2 weeks.