Help: 60-cycle hum on MM Stingray 5

Hello,
I have Music Man Stingray 5 ’98 (ceramic PU and fantom coil). I love this bass, it plays great. But I am very worried about the noise issue. There is 60 cycle hum in parallel mode, but serial mode and single mode are absolutely quiet.
I did a lot to fix this:
1. Connected bass to different amplifiers on different stages;
2. Tried connecting bass with different cables;
3. Inserted several brand new batteries;
4. Checked the soldering on the preamp and pickup, checked the wiring diagram;
5. My bass was shielding with copper foil;
6. Installed a new battery compartment;
7. Installed a new 3-way switch;
8. Installed a new output jack;
9. I also corresponded with EBMM customer support, got a new original pickup and installed it. I checked the new pickup.
BUT … the 60 cycle hum is still there.
It drives me crazy!)
The EBMM customer support guys didn’t find any reason for the 60 cycle hum. They wrote to me about the possibility to put a original newer preamp. Then I would have to install an alnico pickup and pickguard as well, since my preamp version is no longer in production. But I would not want to install an alnico pickup and a newer preamp.
I cannot send my bass to EBMM customer support because I live in Ukraine. Sorry for my English.
So, has anyone had such a problem? Any idea what it could be?