I have two WAY overripe bananas sitting on my counter. I'd love to include them in this. Any ideas on whether that would work...?

I've added bananas along with apples to baked oatmeal and apple kugel, and the combo works really well. So if it were me, I would just replace 1 cup of the apples (or whatever the equal volume is) with the bananas. I've made this cake and it is great!

AJerusalemArtichoke-

There are two ways you could go with this. You could replace the eggs with pureed banana (1/4 cup puree for each egg needed) or you could replace a portion of the oil needed in the recipe. While there is baking soda in the recipe to help it rise, I wouldn't tamper with the eggs since nothing looks more depressing than a flat cake. I'd substitute a portion of the oil for pureed banana...but just be aware since this cake isn't super spice heavy...it could get overpowered with banana.

Here is some advice on the ratio of banana puree to replace oil in a recipe (3/4 cup puree to 1 cup oil) and also provides tips for how to ensure your baked good stays moist since more gluten will form in the batter than with oil.

Hopefully it will help and your cake will turn out just as good!

http://www.livestrong.com/article/538118-banana-as-substitute-for-oil-ratio/