Preheat oven to 350 degrees . Wash chicken and pat dry. Sprinkle inside and out with salt and pepper.
In a large frying pan, melt 3 tablespoons butter over medium heat. Add garlic and cook 1 minute. Add bread crumbs; cook, stirring, until crisp and brown.
Remove pan from heat. Stir in lime juice, lime peel, tablespoon rum, brown sugar, nutmeg, and cayenne pepper; mix well. Add bananas and toss to combine. Stuff into cavity; truss chicken. (Wrap any leftover stuffing in aluminum foil and bake with the chicken.)
Place chicken in a large roasting pan. Melt remaining 4 tablespoons butter and brush over chicken. Roast for 2 hours, until meat thermometer registers 185°. Baste occasionally with pan juices.
In a small saucepan, warm remaining rum. Ignite, and when alcohol has burned off, drizzle over chicken before serving.