Peel and chop the bananas fine, and put them into a small bowl.
Add the remaining tbsp of lime juice, the remaining ½ tsp of salt, and pepper to taste, and toss the ingredients with a spoon to combine this banana stuffing thoroughly.
Pat the chicken completely dry inside and out with paper towels.
Fill the breast cavity with the banana stuffing and close the opening by lacing it with skewers or sewing it with a large needle and heavy white thread.
Fill the smaller neck cavity with the bread-crumb stuffing and skewer or sew the opening shut.
Truss the chicken securely and, with a pastry brush, coat it thoroughly with the 4 tbsp of softened butter.
Place the bird on a rack in a shallow roasting pan just large enough to hold it comfortably and roast in the middle of the oven for about 1½ hours, basting occasionally with the juices as they accumulate in the pan.
To test the doneness, pierce the thigh of the bird with the point of a small, sharp knife.
The juice that trickles out should be pale yellow; if it is tinged with pink, roast the chicken for another 5 to 10 minutes.
Transfer the bird to a large, heated platter, cut off and discard the trussing strings, and let the chicken rest for about 5 minutes for easier carving.
Meanwhile, skim the fat from the juices in the pan and pour in the cup of stock.
Bring to a boil over high heat, stirring to the bottom of the pan.
Cook the sauce briskly for 2 or 3 minutes, taste for seasoning, and pour it into a small bowl.