Combine the flour, salt, and sugar in the bowl of a food processor and pulse 3-4 times. Add the butter and pulse until the mixture looks mealy, 5-6 times. Add the shortening and pulse another 3-4 times. Remove the lid and sprinkle in 5 tablespoons of the cranberry juice. Replace the lid and pulse 5 times. Add more cranberry juice, as needed, until the mixture begins to hold together and pull away from the sides of the bowl.
Dump the mixture onto a clean surface and squeeze together with your hands to form a smooth ball. Divide the ball in half and press each into a disk about 1-inch thick. Wrap each dough in plastic wrap and refrigerate for at least 1 hour. (You can refrigerate longer, even overnight, but the dough will have to sit at kitchen temp for 15 minutes to be malleable enough to roll.)
Peel, core, and slice pears into 1/8-inch slices. Move to a large mixing bowl with 1/4 cup of the sugar then toss with your hands to thoroughly coat. Move the slices to a colander and place inside the mixing bowl to capture any juices. Set aside for 1 1/2 hours.
Transfer the accumulated pear juice to a small saucepan and reduce over medium heat, to 2 tablespoons. Set aside to cool.
Stir the remaining sugar into the pear slices along with the Simple Cranberry Sauce, tapioca flour, lemon zest, lemon juice, salt, and nutmeg. Set aside.
Crank your oven to 400 F and move a rack to the lowest position. Place a 12 x 24-inch piece of wax paper on a clean work surface and lightly dust with flour. Remove the dough disks form the refrigerator, discard the plastic wrap from one and place the dough on the wax paper. Dust with a bit more flour. Roll into a 12 x 12-inch circle, then place into the tart pan, gently pressing the dough into the edges. Set a pie bird in the center of the bottom of the pan and pour the pear mixture evenly around it. Repeat the rolling process with the second disk of dough and place it on top of the pears, letting the pie bird poke through the middle. Press and crimp the edges of the pie together.
Place the pie on a foil lined sheet pan and brush the top of the pie with the reduced pear juice. Bake for 1 hour. Transfer to a cooling rack and let it rest for 2 hours before slicing and serving. (The filling will continue to firm-up over the next 6 hours or so.)
*A pie bird is essentially a ceramic steam stack that allows moisture a way to vent out of the pie during cooking. (The blackbird is the most traditional form, due to the whole "four and twenty blackbirds baked in a pie" business.) If you don't have one, poke around your grandmother's kitchen, it's in there somewhere. Or, you can easily pick one up on the inter webs. Or, you can skip it altogether but your crust will need to be slit a few times to prevent the filling from bubbling over. I also think that baking with a pie bird makes the final pie easier to cut.