Coat 6 (6-ounce) custard cups or ramekins with cooking spray; set aside.
Combine 1/3 cup sugar, 3 tablespoons water, and syrup in a small, heavy saucepan over medium-high heat; cook until sugar dissolves, stirring gently as needed to dissolve sugar evenly. Continue cooking 11 minutes or until golden (do not stir). Immediately pour sugar mixture into prepared custard cups, tipping quickly to coat bottoms of cups.
Place squash in a large saucepan; cover with water. Bring to a boil; cover and cook 12 minutes or until very tender. Drain in a colander over a bowl, reserving 3 tablespoons cooking liquid. Place squash and reserved cooking liquid in a blender or food processor. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters); blend until smooth, scraping sides of bowl. Place pureed squash, 1/2 cup sugar, and remaining ingredients in a large bowl; stir with a whisk. Pour mixture evenly into prepared cups. Place cups in a 13 x 9–inch baking pan; add hot water to pan to a depth of 1 inch. Bake at 325° for 1 hour or until a knife inserted in center comes out clean. Remove cups from pan; cool on a wire rack 15 minutes. Lightly cover and chill 4 hours or overnight.
Loosen edges of custards with a knife or rubber spatula. Place a dessert plate, upside down, on top of each cup; invert onto plates. Drizzle any remaining caramelized syrup over custards.