Crash N Burn ,
Excellent points from a man with obvious experience in the field.
As ham radio operators particularly on the LOW bands (160 and 75 Meters ) running AM we have frequently chased down interference using the same portable AM with a ferrite antenna you described . Once we found the source a call to the power company would usually get us relief.

It may be a good idea for people with questionable power lines to "sniff " the area in the same way you described . There is almost always a quiet part of the AM B'Cast band to give a listen for the popping and frying sounds that come from loose joints in the power line hardware,

As you said the problem is usually worse when dry than wet . Kind of the reverse of what one would expect.