I was able to find the sweet spot for the MW coil on the ferrite rod using an AM signal booster I stumbled across on my constitutional yesterday. For a bit of fun I videoed a demonstration of this signal booster, first MW then LW.
https://youtu.be/aT8Vo4VcdR0
https://youtu.be/yUZTzHhGTKE
Comparing this with a smaller HK AM radio Ingersoll XK-791 which works so much better, see photo, the ferrite rod on this one is only slightly shorter but is thicker, otherwise the component count looks similar. More evidence there is indeed something wrong with this one. By ear I'd say it has a poor signal-to-noise ratio so I'm guessing it's a problem with the circuit around the first stage transistor marked 901. I've no schematic for it but this radio should be simple enough for even me to reverse engineer. More to follow hopefully.