Preheat the barbecue to 350-400 degrees for direct and indirect heating, putting a water pan under the unheated side of the grill.
In a Dutch oven, heat and brown the sausages over the grill, stirring several times, about 12-15 minutes. Drain any liquid into a bowl and transfer the sausages to a bowl using a slotted spoon. Set aside.
In the same Dutch oven, add the cooking liquid and sauté the onions, red and green peppers, and garlic until the vegetables are just limp. Add the stewed tomatoes, stir, and add the bay leaves, green onions, and parsley. Add the Creole seasoning, thyme, and cooked sausage. Continue to stir and add the uncooked rice and water, season with salt and pepper. Mix well.
Bring the water to a boil and cook until most of the water is absorbed, 15-20 minutes, occasionally scraping the bottom of the pot to keep the rice from sticking.
Continue to cook until the rice is tender, stirring and fluffing often with a large fork.
Remove from heat and serve hot.