Make the Baked Pie Shell: Process ¾ cups of the flour, the sugar and salt together in a food processor until combined, about 2 one-second pulses. Add the butter and shortening and process until a homogenous dough just starts to collect in uneven clumps, about 7 to 10 seconds (the dough will resemble cottage cheese curds with some very small pieces of butter remaining, but there should be no uncoated flour). Scrape down the sides and bottom of the bowl with a rubber spatula and redistribute the dough evenly around the bowl. Add the remaining ½ cup flour and pulse until the mixture is evenly distributed around the bowl and the mass of dough has been broken up, 4 to 6 quick pulses. Empty the mixture into a medium bowl.
Sprinkle the vodka and water over the mixture. With a rubber spatula, use a folding motion to mix, pressing down on the dough until it is slightly tacky and sticks together. Flatten the dough into a 4-inch disk, wrap in plastic wrap and refrigerate at least 45 minutes, or up to 2 days.
Adjust oven rack to lowest position, place rimmed baking sheet on oven rack, and heat oven to 425 degrees. Remove the dough from the refrigerator and roll out on a generously floured (up to ¼ cup) work surface to a 12-inch circle. Roll the dough loosely around a rolling pin and unroll into a 9-inch pie plate, leaving at least a 1-inch overhang on each side. Working around the circumference, ease the dough into the plate by gently lifting edge of the dough with one hand while pressing into the plate bottom with other hand. Leave the overhanging dough in place; refrigerate until the dough is firm, about 30 minutes.
Trim the overhanging dough to ½ inch beyond the lip of the pie plate. Fold the overhang under itself; the folded edge should be flush with edge of pie plate. Flute the dough or press the tines of a fork against dough to flatten it against the rim of pie plate. Refrigerate the dough-lined plate until firm, about 15 minutes. Proceed with pie recipe as directed.
Remove pie pan from refrigerator, line crust with foil, and fill with pie weights or pennies. Bake for 15 minutes. Remove foil and weights, rotate plate, and bake for 5 to 10 minutes additional minutes until crust is golden brown and crisp. Place on a wire rack to cool completely before filling.
Make the Filling: Select 6 ounces of misshapen, underripe, or otherwise unattractive berries, halving those that are large; you should have about 1½ cups. In food processor, process berries to smooth puree, 20 to 30 seconds, scraping down bowl as needed. You should have about ¾ cup puree.
Whisk sugar, cornstarch, Sure-Jell, and salt in medium saucepan. Stir in berry puree, making sure to scrape corners of pan. Cook over medium-high heat, stirring constantly with heatproof rubber spatula, and bring to full boil. Boil, scraping bottom and sides of pan to prevent scorching, for 2 minutes to ensure that cornstarch is fully cooked (mixture will appear frothy when it first reaches boil, then will darken and thicken with further cooking). Transfer to large bowl and stir in lemon juice. Let cool to room temperature.
Meanwhile, pick over remaining berries and measure out 2 pounds of most attractive ones; halve only extra-large berries. Add berries to bowl with glaze and fold gently with rubber spatula until berries are evenly coated. Scoop berries into pie shell, piling into mound. If any cut sides face up on top, turn them face down. If necessary, rearrange berries so that holes are filled and mound looks attractive. Refrigerate pie until chilled, about 2 hours. Serve within 5 hours of chilling.
Make the Whipped Cream: Using an electric mixer, whisk together the heavy cream, sugar and vanilla on low speed until stiff peaks form. Increase to medium speed and whip until thick. Pipe onto pie or serve dolloped on top.