1. To prepare crust, weigh or lightly spoon flours into dry measuring cups; level with a knife. Combine flours, 1 1/2 teaspoons granulated sugar, baking soda, and xanthan gum in a medium bowl; stir with a whisk. Cut in butter and shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add milk; toss with a fork until moist. Gently press mixture into a 4-inch circle on 2 sheets of heavy-duty plastic wrap that overlap; cover with additional overlapping plastic wrap. Chill 30 minutes.
2. Preheat oven to 400°.
3. Roll dough, still covered, into a 13-inch circle Fit dough, plastic wrap side up, into a 10-inch removable-bottom tart pan coated with cooking spray. Remove remaining plastic wrap. Press dough against bottom and sides of pan. Line bottom of dough with parchment paper; arrange pie weights or dried beans on paper. Bake at 400° for 8 to 10 minutes; carefully remove parchment paper, and cool crust 5 minutes on a wire rack.
4. Reduce oven temperature to 350°.
5. To prepare filling, combine corn syrup and next 5 ingredients (through eggs), stirring with a whisk. Fold in cranberries and walnuts. Pour filling into crust. Bake at 350° for 45 minutes or until center is set and crust is slightly golden. Cool completely in pan.