Doc,
Your Luger doesn't fit into any particular category. It is unusual, but you will get mixed reviews on whether it is a collectable or not. In all probability it is a "lunchbox special" assembled by a factory worker from various, mostly un-nmbered, parts. Kind of like Johnny Cash's song about building a Cadillac one piece at a time. Somehow it made its way into "official" channels and was reworked for commercial sales. The barrel is numbered to the frame but it is a replacement (note that it does not have a witness mark).
A "variation" is usually considered to be a piece that is the result of authorized production. It may consist of only a few pieces to many thousands, but it has unique features that set it apart from other production "variations". I suspect your Luger is a "one-of-one" produced by who knows? I think you could put a few rounds through it for the fun of it and won't be risking a national treasure.
Good luck and thanks for the photos. To repeat myself, it is a cool gun.