Perhaps
@ScoopKona can give us advice on how he would cook a turkey on a BBQ grill with aluminum foil. I know that it would not be a particularly good way to cook a turkey, but I would like his advice of what he would do if he had to.
A smoker isn't a bad way to go. I've done this before. (I've cooked thousands of turkeys -- everything from deep frying to rotisserie.)
The problem with all turkeys, every single one of them, is that the white meat starts to dry out at 145f. And the dark meat needs a few hours at 165f to render collagen into gelatin. Any solution which has one bird and one cooking method is a compromise. Usually a bad compromise.
So, first thing I'd do is google "Know Whey diagonal split turkey." They do a fine job explaining the problem and an oven-roasting solution. Then I'd modify that for the grill.
Step one is injection marinading the night before. (I like paprika garlic butter. But what you inject is entirely up to you). Works the same as brining, just much faster. Give it overnight in the fridge for all the marinade to distribute. Then you're ready to cook. Much of the marinade will leak out and solidify overnight. I smear that all over the skin prior to cooking.
I would most definitely do indirect heat, or even better, offset smoking. No meat directly over coals -- flare ups will ruin your day. Turkey can take a great deal of smoke, too. Cook the dark meat first. When the dark meat reaches 165f, I'd wrap the legs with foil (or better still, covered in a dry roasting pan). Let the dark meat continue cooking and add the breast. By the time the interior of the breast hits 145f (and you have to hold it there for 10 minutes to kill off any nasties), everything is perfectly cooked.
Put the dark meat (carefully) on a platter. Add your stuffing in the cavity created by the legs and then place the breast on top. Voila! Norman Rockwell turkey -- moist breast, non-greasy thighs. Doesn't look like a turkey which has been cooked in two stages. Best of all, you've made stuffing which isn't going to get everyone sick -- because this is the thing that people get wrong most often.
A good meat thermometer (the leave-in kind) is key to getting this right. You don't want to be lifting the lid often -- cook the legs until 165, remove the thermometer, wrap, add the breast, put the thermometer into the deepest part of the breast, and go for your 145f goal.
