Lightly coat an 8 x 4-inch loaf pan with cooking spray; dust with 1 1/2 teaspoons all-purpose flour. Set aside.
Preheat oven to 350°.
Lightly spoon 1 cup all-purpose flour and whole wheat flour into dry measuring cups; level with a knife. Combine flours, baking powder, baking soda, cinnamon, salt, and nutmeg; stir with a whisk to combine.
Combine sugar and 1/4 cup butter in a large bowl; beat with a mixer at medium speed until light and fluffy (about 3 minutes). Add egg substitute; beat until combined. Beat in banana, rum, and vanilla. Add flour mixture to banana mixture; beat on low speed just until combined. Scrape batter into prepared pan with a spatula; smooth top. Bake at 350° for 30 minutes; gently remove from oven, and drizzle top with 1 tablespoon melted butter. Bake an additional 10 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 5 minutes before turning out onto a wire rack to cool completely.