You've probably already tried a different pick-up...   Sorry, had to mention it.

Way back, in my electronics apprenticeship days my old tutor used to talk of the times before wiring looms and multilayer circuit boards in radio sets.

Wiring layouts were routed in a similar way but not exactly the same in each set.   Sets that 'hummed' during production were sent to a lady with a big crochet hook thing who moved the wires away from any potential RF radiation and then tied them back to stop it recurring.

Any bespoke electronics sometimes needs tweaking and it will be a trial and error thing.   Richard is right , try screening, re-routing and shortening (sometimes lengthening) any leads/wiring.   Tin foil should be adequate but sheets of screening material are readily available from radio suppliers and may be more effective to shield areas.

Good Luck