How about bread pudding? This would provide it with needed moisture.
Plus, Rum goes nicely with bananas so you could add some Rum to the liquid part of the custard in any standard recipe for bread pudding.
Once you have the ratio for the eggs to liquid for the custard down, it’s pretty easy to add in other bits of deliciousness like nuts or chocolate chip bits.
In addition, you could also make some type of rum/cream sauce or caramel sauce to pour over it once baked.
The nice thing is that bread pudding tastes delicious either hot or cold or anything in between.
The possibilities are limited only by your imagination.
BTW: when you say that it baked too long that it’s merely dried out rather than burnt.
If it’s burnt, there is really no way to get rid of that burnt taste. Nothing will disguise it. If it’s just some of the edges and the burnt taste isn’t permeating the whole loaf then just cutting off those parts should suffice.