I think there is one or was listed in the EE at some strange price. I just don't see the cost benefit to do it, but I can buy the originals , so I could be a bit biased
I picked up a nice post war one ,PP, with all the papers, and kit in the box not long ago for under 300.oo
If you want something, look for a browning 1922 in 380cal. and you are good to go.
P.S. I know of a luger a fellow just had converted, he got a barrel from the US, 100.oo he said , new 6 inch.
But the gunsmith that did it had a hell of a time indexing it and getting to feed, changed the mag out and that helped, he said that he hatted the job.
It will not cycle standard ammo, he has to load a bit hotter. The job was 300.oo, this is a mismatch gun , so that could have been the problem .
Re reading your post ,I just figured out you do have 12-6 so forget the browning thing.