Position a rack in the center of the oven and preheat the oven to 350 degrees F.
Put the diced figs in a medium bowl and add the warm water. Let soak until softened.
Whisk the unbleached flour, cake flour, oats, baking powder, and salt together in a large bowl. Set aside.
Put the maple syrup, milk, eggs, egg yolks, and canola oil in a medium bowl and stir with the whisk to combine. Add the mixture to the dry ingredients, stirring with a spoon just until all the flour is moistened. This should be a wet batter, because the oats absorb a lot of the liquid during baking.
Fold the walnuts and figs into the batter (the figs do not need to be drained). Divide the batter evenly between two oiled 9- by 5-inch loaf pans. Bake for about 1 hour, until a toothpick inserted in the center comes out clean. (If your oven bakes unevenly, rotate the pans from left to right and front to back about halfway through the baking time.)
Remove the pans from the oven and use a pastry brush to glaze the tops of the loaves with maple syrup. Set them on a rack to cool for about 10 minutes. Turn the loaves out of the pans and set them on the rack to cool completely before serving. Wrap any leftovers tightly in plastic wrap and store at room temperature. They may also be frozen, wrapped first in aluminum foil and then in plastic wrap or a heavy-duty freezer bag.