I've learned something about covering an entire grill with grill grates. It can get HOT! So tonight when I went to try out some BBQ chicken, I removed one of the grill grates to allow some airflow on either side. This helped lower the temperature a good bit.
Cooked these tonight and for the first time in I don't remember how long, I ended up with FULLY COOKED and NOT BURNT TO A CRISP BBQ chicken!
Thanks to those that suggested that even though it may read 165 in the thickest part, that doesn't mean it's 165 near the bone which cooks last. Finally, BBQ chicken we actually enjoyed!