Add the alligator meat and the onion, celery, and bell pepper, raise the heat to medium-high, and stir vigorously to coat the meat and vegetables with the roux, scraping the bottom. Stirring frequently, sauté the mixture for about 7 minutes, or until the vegetables are soft. In the meantime, bring the chicken stock to a simmer in another pot. Add the garlic to the vegetables, and sauté for about 2 minutes, then add the stewed tomatoes. Stir for a minute, to incorporate, then add the hot chicken stock and wine. Add the bay leaves, thyme, and Cajun seasoning, and bring to a simmer.