My Japanesse Jazz Bass was very noisy when I adquired it so I shielded every cavity with aluminium foil (I had not enough cooper foil at the moment) and placed a star point ground in a cooper strip at the pots' cavity. As a result, the bass is death quiet but the output signal is also very weak now. Prior to shielding I used to set the gain of my amp at 4, now I have to set it at 9 for the same result.
Any time you have gain reduction, it means your signal is somehow getting grounded... maybe a "resistive" ground, but nevertheless. A full short to ground of course would mean no output. Recheck everything and make sure all signal wires are well away from the shielding/grounding, and isolate with insulation or electrical tape as needed.
The other is a MIM Precision which was also a bit noisy. So I shielded the "common" cavity with cooper foil and place a star point ground in it. The result is an "ocassional static current noise". As long as I am touching the strings, there is no noise but, when I am not acting as ground, the noise comes in for one second or so and then disapears.
I have tried several ground connections, as I thouhgt I had a problem of potential differences in the grounding cage, but I think this is not the problem. I suspect that the cause of this problem could be at the pickup.
Note: Pickups' poles are not grounded (nor JB neither P).
Cheers,
You can't introduce a pickup problem by shielding and grounding unless you accidentally short something (see above). Any time you have noise that goes away when you touch the strings, it usually means there's not a good connection to the strings from the ground/shield, meaning the bridge ground wire isn't making a good enough connection (or maybe one at all). Maybe that's always been there, but masked by the other noise you just got rid of. Another thing to check, anyway.
Given that, even with great grounds and shields you can still have cases for noise that reduces or goes away when you touch the strings, but with proper grounding/shielding, it should be "as good as it can get" given a particular playing environment and pickup.
On pickup pole grounding, that can also help, but it can also affect pickup tone, and it's sometimes a challenge to get a ground wire to touch and remain touching all poles equally (and it needs to ONLY be on the bottom of the poles, which may not even be available on all pickup types).
Finally, generally speaking now, just keep in mind there's nothing you can do to completely eliminate hum if you have single coils in a J bass and you don't have both fully blended (which sets up a humbucking configuration). Any time you favor, or especially solo, a single coil, you get hum, period. The amount totally depends on the playing environment, which can vary greatly.