Light 1 side of grill, heating to 400° to 475° (medium-high to high) heat; leave other side unlit, placing disposable baking pan under grill grate. Stir together salt and next 5 ingredients; sprinkle mixture inside cavity and on outside of each chicken.
Reserve just 3/4 cup ginger ale from each can to put toward the 2 cups needed in glaze. Place chickens upright onto each can, fitting can into cavity. Pull legs forward to form a tripod.
Pour water to a depth of 1 inch into disposable pan. Place chickens upright on unlit side of grill above pan. Grill, covered with grill lid and rotating chickens occasionally, 1 hour and 20 minutes to 1 hour and 30 minutes or until golden and a meat thermometer inserted in thickest portion registers 165°. Let stand 10 minutes. Remove chickens from cans, and carve. Serve with Ginger Ale Glaze.