Man, if you get this to work out, you win the Nobel Prize in cooking turkey! It is exactly the same thing that happens in my oven or smoker. I think it is because the AQ is just a well-sealed oven with a smoke generator. The dark meat simply takes longer to cook. I've tried tricks like foiling the breast to start (or to finish) to keep it from overcoooking, and I've heard but not tried starting the bird breast side down then rotating it, but juicy white and done dark meat at the same time seems to be a constant struggle few master. In a recent thread, cal has recommended spatchcocking the turkey, and that is my next experiment.
Interestlingly, with chicken, when I grill halves over low-medium heat, both breast and dark meat are tender and juicy. I'm thinking of grilling a half-turkey to see what happens. It won't be the same as smoking, but at least it will have crispy skin!