Place carcass in a large pot. Add stuffing, onion, carrots, celery, poultry seasoning, sage, and bay leaves.
Pour in chicken broth; add additional water to cover, if needed. Bring to a boil over medium-high heat. Reduce heat to medium; simmer, skimming off and discarding any foam, about 1 hour.
Remove carcass and any bones; pick off any meat. Return meat to the pot and discard bones and skin.
Add garlic salt and pepper. Stir in rice and return to a boil over medium-high heat. Reduce heat to medium and simmer for 15 minutes.
Stir in peas; continue to simmer until rice is tender, about 10 minutes more.
Adjust seasonings to taste before serving.