Is this a single family home or is there other circuit besides "all" the ones you were able to shut down that may be interfering? I once had a inductive transfer that affected a fluorescent. This was caused by a loaded wire next to the switch feed to the future inductively passed the current. I never checked with a volt meter but the 4' fixture would flicker only when a pump was on. There was no conductive path for this current it was inductively transferred. It seems from your tests, You basically have eliminated most other possibilities I am thinking of.
Just a couple suggestions they may help trigger a idea or something.
Hopefully if my suggestions didn't help, someone else in the form can come up with other ideas. .
Let us know what you find!
or maybe supernatural forces are at work. I am sure at this point it seems that way.:confused: