Dirty Rice question- Doing it right?

When I make dirty rice, I sautee a diced bell pepper, a couple of celery stalks, and about 1/2 of a medium onion. Once wilted well, I remove and fry up 2 1lb tubes of hot bulk sausage, seasoning well with salt, black pepper, garlic and some cayenne pepper. I break the sausage up fine while it is cooking. When it is browned, I add the veggies back. I puree a 1lb tub of chicken livers in the food processor, and them to the sausage and veggies then stir until everything is coated and cooked. I mix the meat/veggies into a large bowl with 2 cups of cooked rice a little at the time so everything gets mixed up well.

Is this pretty close to the traditional dirty rice/rice dressing y'all make at home? Any suggestions or other ways? TIA