I didn't have a fine thread Cox needle, so I tried one of the Texas Timers fine needles.
It appears that someone must have forced the Super Tiger needle that came with that engine, and damaged the threads. The TT needle will not screw in more than a fraction of a turn.
I doubt very much that the threads can be cleaned up with a tap, so I'm going to remove the KK unit, and install the original Norvel needle and spray bar.
Bill