Banditman wrote
My suspicion is vibration in the 3 bridge springs somehow being picked up. Solution?
Surgical tubing inside the springs is the best solution I've found. But if your pickups are hearing a lot of the noise, they might also be microphonic.
Earthing problem? Loose earth connection on the bridge?
Earthing problem. Usual suspect is the jack socket, a cable or more worryingly the amp... Shocks are due to ground not being able to be made in the usual fashion and a voltage potential from somewhere.