I bought a BigGreenEgg this summer and have been going crazy with smoking stuff. We've done turkey on it a few times, maybe four, and so far I am *not* convinced that smoke brings anything to Turkey, unlike some other meats like pork and chicken. It might have to do with how much and which kind of wood chips you use.
Smoked pork shoulder is what I did for thanksgiving and roasted a turkey breast in the oven.
When we brined our turkey, we used a very large plastic bag and then tied it and zip tied it. We brined it overnight, put it on a upright stand with beer and seasoning in the cup. Turned out awesome texture and moisture, just wasn't sold on the smoke flavor with turkey.