Martin - I agree with Kitz that it looks like some form of RFI - streetlight(s) fit the time profile and would be fairly easy to yes/no check.
Also, having already taken precautions against front end pickup for other RFI, it is possibly getting in via the power wiring not radiation.
However suggest it is time for a practical test with the MW radio - to confirm the source before looking at the path; logical speculation based on indirect measurements only takes you so far !