Eng you suggested there is a misgrounding somewhere.
I don't know if I'd call it a "misgrounding". But the headphone and microphone circuit grounds could be tied together. Your test appears to indicate that the "loop" is inside the headset itself as opposed to within the adapter.
The next step I'd try would be to find or have built an isolating device. This would be a small enclosure with a plug and jack that would 'break' the electrical continuity of the headphone circuit. Here is an example of a home-brewed device* (for a different but related application):
Application Note: DXD Configuration File Excerpts
If you trace the schematic, you will see that there is no electrical path from the input plug to the output jack. The signals being coupled through the transformers (magnetically). There may be commercial units available with the appropriate plugs/jacks. There are bulkier units with screw terminals and larger enclosures that are not suited to flight deck use. There may also be dual jack to XLR5 adapters made with isolation transformers built in, but I am not familiar with any.
*If your headphones have a mono jack, only 1/2 of this circuit is needed.