Transfer the pie to the hot baking sheet and bake 20 minutes. Pour the berry filling into the crust and sprinkle evenly with the crumb topping. Refrigerate until firm, at least 20 minutes. Roll out the dough into a 12-inch round on a lightly floured surface ease into a 9-inch pie plate and crimp the edge. Place a baking sheet on the lowest oven rack and preheat to 425 degrees F. Make the filling: Combine the berries, granulated sugar, brown sugar, lemon juice, tapioca, cinnamon, cardamom and salt in a large bowl toss well. Refrigerate until ready to assemble the pie. Work in the butter with your fingers until clumps form. Meanwhile, make the topping: Combine the oats, flour, brown sugar, salt, cinnamon and allspice in a medium bowl. Wrap and refrigerate until firm, at least 1 hour or overnight. Turn out the dough onto a piece of plastic wrap and pat into a disk. Pulse in the vinegar and 2 tablespoons ice water until the dough starts to come together but is still crumbly, adding up to 2 more tablespoons ice water if needed.
Pulse in the butter until just combined with some pea-size pieces remaining. Add the shortening and pulse a few times until coarse crumbs form. Make the crust: Pulse the flour, granulated sugar and salt in a food processor to combine.