Does the buzz reduce while touching the pickup case? If so, you might try a resistive connection to ground or earth. A straight wire make be dangerous. A two prong plug to a tube amp may send at least 60 volts to the pickup.
A friend has fender with tripple heads... all single coil. He has the same issue. But, holding the strings seems to tame the buzz. I wanted to try a wireless to see if lossing the cable would break the loop. Never got a chance to do it. Just a thought...
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