Preheat oven to 425 degrees with rack in the lower third. Coat a 9″ glass pie plate with nonstick spray and line a baking sheet with foil.
Prepare pie dough and chill.
Pie dough instructions: Process 1 1/2 cups flour, salt, and sugar in food processor until combined, about 2 one-second pulses. Add butter and shortening and process until dough just starts to collect in uneven clumps, about 15 seconds (dough will resemble cottage cheese curds and there should be no uncoated flour). Scrape bowl with rubber spatula and redistribute dough evenly around processor blade. Add remaining cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 quick pulses. Empty mixture into medium bowl.
Sprinkle vodka and water over mixture. With rubber spatula, use folding motion to mix, pressing down on dough until dough is slightly tacky and sticks together. Divide dough into two even balls and flatten each into 4-inch disk. Wrap each in plastic wrap and refrigerate at least 45 minutes or up to 2 days.
Mash two cups of each type of berry for the filling with 1/4 cup sugar, vanilla, salt, orange zest, and juice.
Process tapioca in a coffee grinder until fine, then mix with the cornstarch and remaining 3/4 sugar. Add cornstarch mixture to the mashed berries; fold in whole berries. Let filling stand.
Roll out one disk of the dough and line the prepared pie plate.
Pour filling into the pie plate.
Roll out the second portion of dough and prepare a lattice top (if desired); trim and crimp edges.
Brush lattice and edges with half-and-half (or whole milk) and sprinkle with raw sugar.
Bake the pie on the prepared baking sheet for 25 minutes on the lower rack.
Reduce the oven temperature to 350 degrees and continue baking until crust is golden and filling is thick and bubbly, 40-50 minutes more.
Cool pie completely before serving.