... and we have a winner!
I am certain that the cause is the combination of those big wound Nordys (excellent, clip, thanks for sharing it mickster) and the stock preamp, which I've identified as an EMG B64 3-band active EQ and they aren't playing together well. I think the Nordy's are causing the 9v EMG pre to clip when everything is up.
I can see why wind these YUUUUGE sounding pickups might cause noise in the designed-not-to-run-this-hot-stock-preamp - it's like putting a 1700 horsepower engine on a stock Camry gearbox. Let off the gas and things will break (OK, try and start that and things would probably break).
Same general idea though.
In the meantime, I'll double and triple check batteries and recheck the string height - excellent suggestions.
So I'll be talking to a luthier soon about upgrading the preamp (I am not a soldering guy) and find some recommendations for preamps to pair with the Nordys.