Okay but do you think that the spark plug adaptor is the cause of that plug to run leaner than the "normal" plug? The adaptor reduces the depth of the plug.
The plug may not be running leaner, it may be running hotter. Take a close look at the ground electrodes of the plugs. There should be a noticeable change in the colour of the deposits on the electrodes, about 3 mm up from where it is welded to the body. The deposits should be darker close to the body. If you can post a picture of the plugs, that would help.