Put sugar into a large mixing bowl, then set aside 1/4 cup. "You need a really big bowl to give you enough room, later, to fold the batter without deflating it." Weigh in or add corn and rice flours to bowl. Add baking powder and salt, then egg yolks, oil, and 1/2 cup water. Add zest of 1 orange and whisk to blend thoroughly. Set batter aside 15 minutes to hydrate corn flour.
Meanwhile, position a rack in lower third of oven and preheat oven to 325°.
Combine egg whites and cream of tartar in bowl of a stand mixer. Using whisk attachment, beat whites on medium-high until they're creamy white and the beater leaves tracks. Slowly sprinkle in remaining 1/4 cup sugar, beating on high speed just until egg whites hold a firm peak when you lift the beater (they should not be dry). "If you're in doubt, think about the egg whites as balloons. The more beaten and expanded they are, the more likely they are to break in the oven (since the heat will expand them even more). Underbeating is better than overbeating."
Scrape half of egg whites onto corn-flour batter and fold in until they are partially blended, using this gentle technique to keep from deflating the whites: "Cut down the center with your spatula, scrape under the batter and up the sides of the bowl, and then lift the batter and let it drop over on itself." Fold in remaining egg whites just until batter looks blended. Scrape batter into a 10-in. (10 to 12 cup) tube pan with removable bottom (ungreased) and spread evenly. "An ungreased tube pan lets the batter climb the sides."
Bake until top of cake is golden brown and a toothpick inserted into the center comes out clean, 45 to 50 minutes.
Meanwhile, squeeze enough orange juice to measure 6 tbsp. In a small bowl, stir orange juice, lemon juice, honey, and orange-flower water together.
When the cake is done, set the pan on a rack. Immediately slide a very thin spatula around sides of pan, and a thin skewer around center tube, to detach them. Poke cake all over with skewer and slowly spoon orange mixture over cake, letting it sink into holes and run over the sides. Let cake finish cooling in pan.
To remove cake from pan, lift tube, then slide a thin spatula between cake and removable bottom, pressing against the bottom to avoid tearing cake. Lift cake off bottom: Cut a manila folder in half crosswise, then slide on either side of cake between pan bottom and cake. Or, use two metal bench scrapers. Slide your hands underneath the folders or scrapers, and lift cake off tube to a serving platter. Top with whipped cream topping and candied orange zest, and slice with a serrated knife.
*Find orange-flower water at well-stocked grocery stores and online.
Make ahead: At least 3 days at room temperature, still in pan and wrapped as airtight as possible; up to 3 months frozen, removed from pan and wrapped well. Bring to room temperature before serving.
Note: Nutritional analysis is per slice (1/12th of cake).
Each flour has its own character, so it doesn't always work to substitute. Also, it's key to weigh the flours--they can fluff up or settle, which throws off a volume measure. (For more, see sunset.com/weighing.) Find at well-stocked grocery stores, bobsredmill.com, or authenticfoods.com.
White Rice Flour: Milled from rice that's had the bran removed. Produces fine-crumbed cakes and silky puddings; amplifies flavors.
Brown Rice Flour: Has the structure-building properties of white rice flour, plus a slight graininess and toasty caramel flavor.
Oat Flour: Powdered oatmeal, with a sweet, butterscotchy flavor. Makes tender cakes and delicate cookies.
Buckwheat Flour: From roasted whole buckwheat seeds. Typically earthy, but can be delicate and floral depending on how it's used.
Corn Flour: From whole kernels; not to be confused with cornstarch. Yields baked goods with sweet corn flavor and lovely pale gold color.
Xanthan Gum: Not a flour but a natural bacterial by-product. Often used with gluten-free flour to thicken and give structure.