Peel butternut squash and papaya using a julienne slicer or vegetable peeler. Continue to peel the flesh into lengthwise strips, rotating the squash and papaya, until all the meat is sliced. Arrange the longer strips of squash along the bottom and sides of a large, deep glass baking dish until covered. Layer jicama over squash layer. Cut remaining squash into 4-inch long strips and set aside.
Heat cream cheese in a saucepan over low heat until smooth and pourable, about 5 minutes. Stir honey into cream cheese until evenly combined; pour over jicama layer.
Heat 2 tablespoons butter in a skillet over medium heat; saute reserved squash until soft and fragrant, about 7 minutes. Layer squash over honey cream cheese layer.
Heat remaining 1 tablespoon butter in the same skillet and saute bananas, cinnamon, brown sugar, and nutmeg until bananas are slightly browned and brown sugar is dissolved, about 3 minutes. Pour banana mixture over squash layer. Cover top with papaya strips.
Bake in the preheated oven until cooked through and bubbling, about 1 hour.