I just ground all my pots and switches using the least wire necessary to the jack. I haven't relied on the the pickguard shielding for ground. It should work fine either way, but I'm no expert.

In your case, it's only your strings/bridge that seems to be a problem. I thought we determined it was dirty power, or something? There is a practice of using a fuse or cap on the bridge ground to guard against potential electrocution. It might be worth looking into.