Heat remaining olive oil in the pan. Add tomatoes, onion, chorizo, and garlic. Cook until tomato juices are mostly reduced, 5 to 10 minutes. Stir in remaining paprika, turmeric, saffron, and oregano. Add rice and cook for 5 minutes. Pour in 4 cups chicken stock; increase heat to high. Stir once and close the grill lid. Cook until the rice on the bottom becomes crispy, about 8 minutes.