With respect, Montana is in fact among the farthest states in the Mountain West from North Carolina you could have chosen, excepting Idaho.
But if you want to go to Montana just because you want to go to Montana, that's fine. Just be willing to pay a potentially higher travel cost, if for no other reason than Montana lacks a major air hub like Denver or Salt Lake, meaning you'd likely have to tack on the cost of an extra connecting flight just to get there if you're flying. And if you're driving, well, the extra distance requires more gas.
Have you ever considering "ruffing it" in the Western part of NC? My sense from reports is that the ruffed grouse population on the NC side of the TN-NC state line has a decent grouse population, if you're willing to walk in excess of 7 miles or more in high elevation during a hunt.