Heat a large pot over medium-high heat. Add bacon, and cook until crisp. Remove bacon pieces with a slotted spoon, and set aside. Add celery, bell pepper, and onion to the bacon drippings, and cook until tender.
Add the ham, chicken and sausage to the pot, and pour in the tomatoes, beef broth and chicken broth. Season with thyme and Cajun seasoning. Bring to a boil, and add the rice. Bring to a boil, then turn the heat to low, cover, and simmer for about 20 minutes, until the rice is tender.
Stir in the shrimp and bacon just before serving, and heat through. If you use uncooked shrimp, let it cook for about 5 minutes before serving.