Help me ID this home build Luger carbine 1920 patter?

[Bluefeather300]

Dont know if this is the right place to post but i think at its base its a commercial?

So I acquired the other day a home build 1920 pattern(?) Luger carbine and just had a few questions and to see what you guys thought.

My determination of it being a "home build" is the serial #82091, the forestock extension is soldered on, the rear of the toggle still has a sight on it, and there is no helper spring in the forestock or forward barrel lug for the helper.

now that being said im not really sure what this was to begin with. I received it with zero internals and polished out. It had the complete bolt number match 91 and toggle marked DWM w/ crown over the "N" and matching number on the rear toggle 91, the forestock w/ zero markings, grips marked GSX and the complete serial #, and the trigger side plate with matching number 91. All the internals (and I switched the side plate and safety side grip) came out of my 41 byf P08. The unit is chambered in 9mm and not 30 luger and there is an "A" stamp at the lug under the barrel and a "D" stamp at the rear of the receiver after the rails.

Any thoughts or suggestions and any sources for the Carbine style rear slider sight (im thinking thats going to be the hardest piece to come by) as I do want to complete the gun