For a 9 inch pie, two tablespoons of AP flour and 2 teaspoons of cornstarch will make a pie that holds together nicely and doesn't shed juice when cut, but is not too stiff either. Another excellent technique is to cook the filling beforehand and let it cool, then add to the pastry and bake the pie. This makes for a less soggy bottom crust. For 2 1/2 pounds of apples, in addition to the starch, that's 2 Thb of butter, 2/3 cup sugar, 1/2 tsp cinnamon, 1/2 tsp. nutmeg (or mace), a bit of salt.
Save the tapioca for berry pies.
I've never tried sweet rice flour, but in my experience, regular white flour works just as well. Since it has so much gluten and doesn't absorb quite as much liquid, you generally have to double the amount of flour (if the recipe calls for 1 T of cornstarch, use 2 T flour). Also, flour doesn't turn as clear as cornstarch does when it cooks, so your finished pie might have a cloudier filling -- but it should still be just as delicious.
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Save the tapioca for berry pies.