Instead of dry brining the turkey, rub the turkey with the BBQ rub. There's plenty of salt in that to do the work. Let sit for 24 hours.
Instead of preparing the oven, prepare the smoker. For me - it's the Big Green Egg. Use the same temp as the Roasted Turkey Recipe - 320 degrees. Apple wood chips are outstanding.
Add apple wood chips, and Smoke until the breast temperature reaches 165. There's no basting.