How much metal is part of your home's costruction? Roof, exterior walls (metallized insulation, wire mesh under stucco, etc.), interior walls (are the studs wood or metal?), etc., etc.
>>I have a large home on a hill in a fairly isolated peri-urban area, which I wouldn't expect to be subject
>> to massive interference.
>> However, I also have >500 electronic devices, either plugged-in, on battery or hardwired.
I think that is your problem!!!!
Turn every thing off and test each system in isolation.