We substituted a stuffing mix for homemade cornbread in Dolores's dressing.
Remove giblet packages from chickens, and reserve for another use. Rinse chickens, and pat dry; remove excess fat and skin. Place 1 chicken and 1/2 cup balsamic vinaigrette each in 2 large zip-top plastic freezer bags; seal and chill 8 hours, turning occasionally.
Remove chickens from vinaigrette, discarding vinaigrette; pat chickens dry.
Melt butter in a large skillet over medium heat; add chopped green onions and celery, and sauté until tender. Remove from heat. Stir in cornbread stuffing, broth, chopped parsley, and pepper. Stuff each chicken with half of mixture, and tie ends of legs together with string; tuck wing tips under. Place chickens, breast sides up, in a roasting pan.
Stir together molasses and hot sauce. Brush chickens evenly with about 3 Tbsp. molasses mixture.
Bake at 350° for 1 hour and 45 minutes or until an instant-read thermometer inserted in thigh registers 180° and internal temperature in center of stuffing registers 190°. Let stand 10 minutes. Garnish, if desired.