For the pie: combine apples, 1 c sugar and salt in colander set over large bowl. Let sit, tossing occasionally, until apples release their juice, about 30 minutes.Press gently on apples to extract juice and reserve 3/4 cups.
Adjust oven rack to lower-middle position and heat oven to 350. Pulse animal crackers and remaining 1/2 c sugar in food processor til finely ground. Dust counter with cracker mixture. Brush half of 1 pie round with water, overlap with second pie round, and dust top with remaining cracker mixture. Roll out dough to 19x14 inch rectangle and transfer to rimmed 18x20" baking sheet.
Brush dough with butter and refrigerate; repeat rolling process with top crust.
Toss drained apples with tapioca, lemon juice and cinnamon and arrange evenly over bottom crust, pressing lightly to flatten. Brush edges of bottom crust with water and arrange top crust on pie. Press crusts together and use paring knife to trim away excess dough. Use fork to crimp and seal outside edge of pie. Then pierce top of pie at 2" intervals. Bake until pie is golden brown and juices are bubbling, about 1 hour. Transfer to wire rack and let cool 1 hour.
GLAZE: While pie is cooling, simmer reserved apple juice over medium heat until syrupy and reduced to 1/4 cup, about 6 minutes. Stir in lemon juice and butter and let cool to room temperature. Whisk in confectioners' sugar and brush glaze evenly over warm pie. Let pie cool completely at least 1 hour or longer.