I would try to find the orientation of the existing magnetic field in the pickup by using a gauss meter or determine alignment and polarity of the magnet or magnets used. I would remagnetize the pickup with an opposite polarity it originally had. This would change the polarity magnetically and make it in phase with the existing pickup.

If a pickup has no exposed metal parts or poles that might be grounded, I would try to reverse the hot and shield wire close to the pickup. Sometimes the single conductor wire may have a second conductor cut off inside the cable where you can’t see it. If you reverse the hot and shield wire at the pickup, the coils inside could be surrounded by a shield or other hardware that could hum or even buzz if you touch the cover.