MikeW (tounge firmly in cheek) suggests:
Can we have a couple more tests, please?
(a) What happens when you fly inverted and try both antennas?
(b) And do you get the same results when flying in the Northern hemisphere?
Actually test A might show provide a clue if something heavy (engine) is
involved the change in gravity vector might exacerbate/reduce the vibration.
Would actually try 90 degrees (on edge) as well if possible.
I would love to volunteer to be radio man for that test but live in wrong hemisphere so have to aggre that idea B should be tried as soon as possible as well
While removing the ADF keep a sharp eye out for any other possible intermitant contact areas, cowlings or whatever. Even a thin slot can act as an element in antennas.
While likely would not show anything you could also try ligthly tapping the entire top of plane with a rubber mallet parked pointing to tower ( engine off!!) while listening to radio in an attempt to locate the problem.
Whatever is causing the issue is almost certainly outside of or part of airplane skin and on top half.
There is a chance that it is behind the antennas since it could be acting as a reflective element. The active element in a yagii usually has one larger "reflector" passive element behind it
That would fit a bit with the problem not being heard at base station.
Adding additional point:
I just looked at the picture of the airplane (checking for ADF antenna) and noticed the rear window geometry is such that it could be that directional effect happnes when the antenna is "looking through" the cockpit. This means that the culprit "could" be in the cockpit.
A quick test would be to cover the read window with aluminum foil when the problem is occuring (rear seat passenger needed - again I volunteer).
That said the position of the ADF antenna (if it is where/what I think it is in picture) fits well with the theories, you might try tying some non-conductive fishing line to it and give it a good shaking while on the ground to see if it has an affect on radios.
BTW If it "twangs" when plucked (like a guitar string) at about 40Hz (or multiple) it could be mechanically resonating with the prop vibration in flight. 2400 rpm == 40Hz
Good luck and keep up the reports.