In a bowl, mix ketchup, Worcestershire, sugar, coconut milk, water, and hot sauce. Set aside.
Heat a large skillet over high heat. Saute vegetables in the olive oil; first the carrots, then onions, red peppers, garlic, and last, the thyme. Saute until fragrant. Turn the cooked vegetables out onto a dish.
Reheat skillet, adding more oil if necessary. Saute cod until almost done, add to vegetables.
Reheat the skillet. Add the ketchup mixture, and bring to a boil. Add back the vegetables and cod. Stir in the rice, mixing well. Keep moving the rice, like a stir-fry.
After a few minutes, add the crawfish, pigeon peas, and the scallions. Season, to taste. Scatter the shrimp on the top of the rice. Cover the skillet and put it into the oven for about 15 minutes. Cook until shrimp are opaque, and slightly curled.