Place the turkey carcass in a large, deep pot, and add the stuffing, celery, carrots, onion, bay leaves, poultry seasoning, sage, water and chicken stock. Pour in additional water if needed to cover. Bring to the boil over medium-high heat; reduce heat to medium, and simmer for about 1 hour, skimming off any foam. Remove the carcass and any bones. Pick any meat off and return to the pot, discarding bones and skin.
Season to taste with salt and pepper. Stir in the rice and return to the boil over medium-high heat. Lower heat to medium, and simmer 15 minutes. Stir in the peas, and continue to simmer until rice is tender, about 10 minutes more. Adjust seasonings to taste.