Humming and buzzing could become a nightmare. Have you simply tried to find the non-noisy position (because there is one) by slightly moving in circle from left to right ?
That said, to date, the only basses totally quiet I've owned are the Leduc's with their patented hum-cancelling dummy coil à la Alembic (which are also dead quiet) and my old Tune BEB-6 with their own home made quad coils pickups and original twin preamp. When I write dead quiet, I mean in very electrically polluted with LED lights, neon lights, switching power supplies, ...
Ask @Marcoelwray what Delano pickups (same configuration as yours, but with 4 strings) he could recommend you, as on his Elwray Infinga, they are very quiet, powerful and articulated sounding. The bass pass around review is here with some videos :