Submarine vet,
I am sorry to be the bearer of bad news for you...
While I agree that you have a very pretty shooter, I am really sorry that I must inform you that the barrel is not original...
Please compare your gun (located in the bottom photo) to the artillery that is not in such good finish (in the top photo)
It appears that your gun has had a new long barrel installed and had a portion of an original artullery barrel shaped and fitted to the top in order to hold the rear sight in the proper position.
The dovetail on a genuine artillery luger is machined directly into the barrel that has been manufactured specifically for an artillery Luger.
I don't know what you paid for your artillery but if originality is important to you, then you have not achieved your purpose... someone has taken advantage of your enthusiasm...
You can see another example of a genuine artillery luger barrel by visiting the old Owner's corner pages and looking at mine... there are also other artillery lugers in the owners corner with which you can compare your gun.
One last thing, the slide on your rear sight has been improperly assembled. The push button should be on the left (see upper photo).