Eureka! I think I've finally gotten this down.
This banana bread, to me at least, tastes just like what I'm used to: the banana bread my mom always made for us growing up. And yet it's made with all whole wheat flour, olive oil instead of Crisco, and honey instead of sugar!
Here's the recipe:
1 cup overripe bananas, mashed
1/3 cup olive oil (or melted butter or coconut oil)
1/2–2/3 cup honey (depending how sweet you like it)
1 3/4–2 cups whole wheat flour (white wheat, if possible)
2 tablespoons plain yogurt
2 eggs, beaten
2 teaspoons baking powder
1/2 teaspoon salt
1/4 teaspoon baking soda
Mix bananas, oil, yogurt, honey and flour. Add up to an extra 1/4 cup flour if batter is too runny. Let soak 12-24 hours. Preheat oven to 350. Beat in remaining ingredients and pour into buttered loaf pan. Bake for one hour until toothpick comes out clean.
As I said, I think you'd be able to substitute a cup of pumpkin or zucchini or whatever suits your fancy. With those, I'd add a teaspoon of cinnamon and 1/4 teaspoon each nutmeg, cloves and ginger.