Preheat the oven to 375 degrees F. Place a wire rack on a rimmed baking sheet.
Pat the game hens dry and place on the prepared rack. Mix the butter, 1/3 cup maple syrup and 2 tablespoons brown sugar with the salt and all the spices in a bowl. Rub the birds with the butter mixture, making sure it gets in all the cavities and under the skin. Reserve any unused butter for later. Sprinkle the hens with a little extra salt and paprika.
Roast for 30 minutes, then baste with the juices at the bottom of the baking sheet, or a little of the remaining butter. Return to the oven and roast until the juices run clear and an instant-read thermometer inserted in the thigh (do not touch bone) registers 165 degrees F, another 15 to 30 minutes more. Remove the hens to a cutting board or serving tray to rest and remove the rack. Pour the dry sherry into the hot baking sheet and use a wooden spoon to scrape up any browned bits; add a little of the stock if necessary. Transfer the sherry mixture to a small saucepan and add any remaining butter. Melt over medium heat. Meanwhile, mix the cornstarch with 2 tablespoons chicken stock in a small bowl to make a slurry. Add the slurry and the remaining stock to the saucepan along with the remaining 1/3 cup syrup and remaining 2 tablespoons brown sugar. Cook, whisking constantly, until the mixture thickens, about 5 minutes. Serve the game hens with the sweet and spicy gravy.
Be sure to remove the necks and giblets from the cavities of the game hens before trussing. Discard or reserve for another use.