Just to throw a "dash" into it, maple syrup instead of brown sugar can make it just a bit more "Canadian"...
To answer the BBQ hood question thing, lets think outside the box a minute...
If we remove the BBQ grill(s), and set our chicken(s) upon the oven broiler pan, mostly these will fit into the depth of the BBQ lower than the statutory grill racks, at least adequately to give the necessary "overhead" clearances...and catch the runoff juices enough to create gravy (get inventive, and add water to the pan, or stock, or whatever...you're all cooks!) as well as giving this convenient "platform" to pull the "work" out of the heat at the right time...
As a side note, even if I don't, personally, do it like this, if you fill the broiler pan with water/stock/beer whatever, aside from "beer-butting" the chickens (see my post elsewhere!) with the BBQ hood closed, this creates a moisture intense cooking arena, and will give you super moist results, if not the crispy skin feature...your choice of what you are aiming to achieve!
Curiously, most roasting pans from conventional ovens fit nicely to BBQ's, with the ability to insert and remove them...Coincidence? I think not! Just crafty BBQ designers!
Once you have gone this far, so as to insert the bird in the BBQ, lets add some wood chips that are well soaked...hickory is my preference, but alder is "interesting", and the old reliable mesquite works, if less satisfactorally...
John