That sounds like a pretty good start to your plan! I wish I had experience with wild birds but I never get to hunt them or when I see them they are out of season.
If you brine and inject with butter I don't think you'll have an issue with the areas that aren't covered by the skin. I smoked turkey parts as well as chickens (skin removed from the breast sometimes) and chicken parts that are brined and not injected at straight 325F all the time. The uncovered parts are fine.
I would caution to keep an eye on the amount of salt content you are adding. If you are doing a brine (has salt), should you inject using salted butter, then you rub the bird with more salt, and finally finish with a sauce that may have salt, I think you may get salt overload.
Keep an eye on the salt and I think your 200F to 325F would be fine. Heck you may want to do 190F rather than 200F to begin with since birds cook up so quickly. I've had to do that with poultry and smoked pork loin chops just to get enough smoke on them before they finish... they cook up quicker than you think even at low temps!