There is a reason you keep finding information that shoots down your brining idea for a Butterball turkey. Brining is for fresh turkeys - look on the label for the word "fresh" and the "ingredients" label on the back to make sure the ingredients don't include the words "broth" or "salt"- the only ingredient should be "turkey" if you want to brine it. Self-basting turkeys are already loaded with all the salt they need - brining will make them too salty! Same goes for Kosher turkeys.
I'm not sure that your zest in the brine would really do that much good anyway. The flavor in the zest is an oil - and oil and water don't mix. It sounds like what you are really wanting to make is a marinade - which would be high in salt but also includes a large proportion of oil that could carry the citrus flavors into the meat along with the voodoo that the salt does.
I would go along with the idea of tossing some chopped citrus into the cavity (and make dressing instead of stuffing) and either place zest, or make a compound butter with zest, and put it under the skin. Another option might be to place thin cross-section slices of your citrus fruit under the skin.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain