I have a mid-70s Leica-threaded J-12 currently mounted on my CV Bessa R. I have read in many places that this is impossible and in others that it is achievable. The trouble is the huge variation in glass used in J-12 manufacture. So I wonder how much space is lost in a postwar Contax and whether it really excludes all J-12 builds given the glass variations? I really don't know, but given the CV cameras actually have 2 shutters I wonder if the Contax IIa has greater shutter thickness?
If the J-12 glass was known to be a short version, is it worth trying?
The testing plan on a Leica thread camera is to have the lens at minimum focus when mounting it, to open the shutter and watch the lens come through. Some prefer the shutter closed.
Of course the risk is to the lens and the shutter when it closes, so another option would be to make a paper cylinder the exact depth of the mount-to-shutter distance in the camera and place that around the lens, checking the protrusion by eye. You could double check vs the Kiev using the same technique to be sure the technique was working.