Welcome to the forum
Re your Kü luger, is the Kü before or after the serial number.
You are correct that the Kü marked lugers origin is a very controversial topic.
The theory that the Kü marked luger is Krieghoff related because of the luftwaffe acceptance stamps on the receiver, frame and barrel has been dismissed by Randall Gibson himself based on his extensive research into Krieghoff pistols.
Their is also another theory that the Kü is an reject acceptance of assembled Mauser parts that went to the Hungarians who during WW#2 were allies to Germany.
The theory that the Kü stamp belongs to the Kustenfliegerstafflen is one that has not been explored in great detail however if you follow the normal course of Germany and her allies the luger was seldom carried as an airman's sidearm due the weight and bulk of a luger. The airman usually equipped themselves with private purchases of smaller arms in the event they were shot down.
Following this reasoning if the Kü stamp was for the (Coastal flying crews )kustenfliegerstafflen why do we not find any Krieghoff manufactured lugers with the Kü stamp as Goehring was both in charge of these crews and the Luftwaffe in general.
My personal beliefs on the Kü marked lugers is a Mauser contract made during the latter days of luger production.
The frame exhibits no krieghoff machining or marking so I fully support Mr. Gibson's findings ( not a Krieghoff)
The luftwaffe acceptance proofs on the barrel and the frame and receiver is one that should not be overlooked, just because it is luftwaffe proofed a krieghoof it does not make.
41/42 is Mauser acceptance codes and the frame exhibits mauser machining, not leftover DWM parts or any other manufacturer which is another theory.
The Hungarian contract is one that I tend to support although it is in it's infancy as far as research goes.
The Germans were gearing up for an all out assault against the Russian forces in 42 so it would not suprise me to find out if some of the late production were procured by the Luftwaffe and sent to Hungary.
This theory however does not stand up to the serialization of earlier marked Kü lugers.
I own one Kü marked luger and will be posting pictures in a couple of weeks or so.You will find two pictures under mauser lugers in the same heading as yours.
I fully realize that you are now more confused than when you asked the question, but as you said Very controversial subject.
Another possibility that I just realized is that Kufstein was a plant in Austria that was turned over to the Krieghoff authorities by the luftwaffe under decree that they would be utilized by the firm.
This thought could be the reason that the lugers were luftwaffe proofed and bears a strong possibility to the fact that some Kü marked lugers bear the Mauser inscription of spare parts (42)
Mauser manufactured parts could have been transported to this plant when Mauser started assembling the P38 full time and did not have time or choose to assemble the piecesa in their plants.