LK - I've done several turkeys on TheBeast, a KK BB 32. Every one was easy peasy. No problems at all and it's dead simple.
I brine my birds AND i inject. Yes, both. Starting two days ahead of when I want to eat the bird, for my brine I generally use salt, sugar, some herbs ... rosemary & thyme come to mind, some citrus peel ... orange and lemon, and let it sit overnight.
I then pull the bird and let it dry in my refrigerator for a day. You want the skin bone dry. Then the day of the cook I oil the skin with a high temp oil, generally grape seed oil and I inject with butter, garlic, onion, and powdered thyme or rosemary or sage and some maple syrup. Notice there is no stuffing in the bird cavities. I will also ice down the breasts so that they are done around the same time as the leg'/thighs.
I bring TheBeast up to 350F and let it heat soak a couple of hours.
Then it's on the grate with some maple wood for a light smoke. At 350F it takes a 20# bird something like 2:45 - 3:00 hours to reach my pull temp of about 155F. Thermal momentum will carry it to 165F easily. You'll get a nice crispy skin on a turkey with the 350F and grape seed combo.
I don't do low-n-slow on turkey ... the temp doesn't get the skin temp high enough to crisp up. Also, most meats only absorb smoke until the outside of the cook hits 170 or so. Nothing much happens after that, so a long low-n-slow doesn't gain you very much.
Have a wonderful and happy Thanksgiving!