Into a bowl sift together the all-purpose flour, cake flour, sugar, and salt. Blend the butter and shortening into the dry ingredients with your fingertips or 2 knives until the mixture resembles meal. Mix in the almonds. In a small bowl beat together the egg, the heavy cream, almond extract, and vanilla. Add just enough of the egg mixture to the dry ingredients to form a dough, toss it with a fork until it is incorporated, and form the dough into a ball. Wrap the dough in waxed paper and chill it for at least 1 hour. Cut off slightly more than 1/2 of the ball of dough and on a lightly floured surface, roll it into a round about 12 inches in diameter. Lift the dough over the rolling pin and transfer it to a 9-inch pie plate, draping the excess dough loosely over the sides. Let the dough set for 10 minutes. Press the dough firmly into the plate and trim the excess, leaving a 1-inch overhang. Brush the shell with the egg mixture and reserve what remains. Chill the shell and the remaining dough overnight.
In a large bowl combine the cherries with the sugar, cornstarch, lemon rind, almond extract, and salt. Let stand for 30 minutes. Drain the mixture into a bowl, measure the juices, and add water if needed to measure 1/4 cup. Toss the filling lightly and pour into the shell. Preheat the oven to 425 degrees F. On a lightly floured surface, roll out the remaining dough into a rectangle 10 inches long and 1/8 inch thick. With the pastry wheel or a large sharp knife cut out 10 10-inch strips about 1/3 inch wide. Moisten the rim of the shell with water and press firmly on the strips in a lattice pattern. Crimp the overhanging dough into a decorative rim. Brush the strips with the reserved egg mixture. Bake the pie in the lower third of the oven for 20 minutes. Reduce the heat to 375 degrees F and bake the pie for 30 minutes more, or until lightly browned. Transfer the pie to a rack and let it cool slightly.