Preheat oven to 375°.
Combine first 3 ingredients in an 11 x 7-inch baking dish coated with cooking spray. Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, oats, coconut, sugar, ginger, and salt in a bowl; cut in butter with a pastry blender or 2 knives until the mixture resembles coarse meal.
Add 1/3 cup oat mixture to banana mixture, stirring gently to combine. Sprinkle remaining oat mixture over banana mixture.
Bake at 375° for 30 minutes or until lightly browned and bubbly.
If you don't want to use rum, you can still achieve a tropical flavor by using 1/4 cup pineapple juice in the fruit mixture.