The left hand thread may be reluctant to engage, but there is no doubt it won't just pull out and come through the unit, hence Mr G's frustration. The thread is supposed to engage with the ATD centre, and as the bolt moves up the armature thread, pushes the ATD from the armature taper.
A drilled and tapped hole into the end of the troublesome bolt would allow a smaller setscrew to push against the armature shaft and either draw off the ATD, if you're lucky, or remove the offending bolt ready for plan B if you're not. In practice the troublesome bolt needs to be clear of the armature thread, which may not always be the case.
Not saying this is ideal, and armatures do not like big hammers, but it could be a possible solution where the extracting threads slip or do not engage as designed, or lockup with some interference between the bolt left hand thread and the ATD centre left hand thread.
Priory Magnetos have a simple illustration of what goes where and how this infernal so called self extracting device is supposed to work. Look in the ATD Section.
Swarfy.