Question: what are you cooking the chicken in before adding the sauce? You should cook the chicken in the root beer. And turn that /into/ your barbecue sauce. I recommend using root beer, onion, herbs and spices, maybe garlic, carrot, and maybe parsnip, tomatoes, etc. Chunk the onion, carrot, and parsnips, finly mine the herbs and garlic. Herbs not good to eat go in a bouquet garni (cheesecloth satchel that contains herbs/spices), otherwise you don't really need to bother. Cook it uncovered in the rootbeer (you don't need more than what you have listed). I recommend adding tomatoes and a splash of vinegar, and maybe worchestershire. Spices I recommend: cinnamon, nutmeg, chili, chocolate, ginger, mustard, cumin, paprika, just use your brain to combine flavors off that list. Or just use all of them and make mole! (that takes a loooooot longer than 3 hours to make it right though). Combine everything, and cook for at least 4 hours, uncovered on high. You want to cook it long enough for the chicken to basically fall apart, and the sauce to thicken with reduction and with the addition of fat from the chicken. You may want to add some thighs as well. And you know what? Bone in is better.... Feel free to eat the veggies as well.