Why worry about bananas rotting in your beer? How many homebrewers rack onto other fruits like oranges, grapefruits, cherries, and even pumpkin for several weeks, to even longer (think kriek/lambic)?? What harm is done and what rotting have you other brewrs seen? It will be fine.
I say peel and mash a few bananas and a pound of extra 6 row in your mlt, and then maybe even add some to the fermenter after you've reached FG.
BTW, I'm not bashing those of you who have mentioned utilizing yeast profile to get banana esters, thats also a good point.