I've finally come up with a banana bread recipe that can be wheat-free, is at least relatively healthyish and, in Ms. Mango's and my opinion, is quite tasty.  Here it is:

Combine 1½ cups flour, 1 cup sugar, 1½ teaspoons baking soda, and ¼ teaspoon salt.  Use a food processor, two table knives, or a pastry blender to cut in ¼ cup cold butter.

In a separate bowl, mash 4 very ripe bananas, leaving a few small chunks of banana if you desire.  To the bananas, add 4 eggs.  Beat well.  Fold in the flour mixture and mix until just blended.  Transfer to a greased loaf pan and bake at 350° Fahrenheit for 90 minutes.

I have tried all the following variations with excellent success:
- Add ½ cup of chocolate chips or chopped nuts.
- Replace some or all of the flour with a non-wheat flour such as barley flour.
- Replace the butter with shortening for a non-dairy version.
- Use an alternative sugar such as evaporated cane juice.

"Did you just...un-veganize a vegan recipe...?"
"Er...yeah, I guess I did.  Still want to marry me?"