Preheat the oven to 350 degrees Fahrenheit. Then, in a large bowl, start soaking your cake pan strips in cold water (this is optional). Lightly grease your three 9-inch round cake pans, then line the bottom with a round piece of parchment paper, and lightly grease the parchment paper, then set aside. Put all of your desiccated coconut into a large frying pan and heat over medium, stirring frequently, until coconut is lightly toasted (it will smell fragrant and turn golden - not brown!). Once toasted, pour into a medium bowl to cool.
In another large bowl, whisk together the coconut milk, vanilla and coconut extracts, and oil until smooth. Add in the flours, starches, salt, baking powder, baking soda, and cooled toasted coconut and mix until combined.
In a separate clean large bowl, beat the egg whites until stiff peaks form (this will take up to 10 minutes), then slowly fold the egg whites into the cake batter ⅓ at a time until fully combined and smooth.
Set batter aside, and then fasten your now-saturated cake pan strips around the outside of the cake pans (I turn the cake pans upside down to do this). Then pour the cake batter into the three prepared 9-inch pans and bake for 30-35 minutes until a skewer inserted into the center of a cake comes out clean. Let cakes cool completely before turning out. Once cooled, turn out cakes, wrap cakes in plastic wrap, return to pans, and freeze for at least 2 hours (this will make construction a lot easier).