Apparently the Fender Wiring scheme on almost all passive Jazz Basses involves grounding the jack through its contact with the control plate, which seems to be working pretty miserably. Probably something no other brand would do, but possibly that no other brand could get away with. There's only one Fender after all. When I had both pickups on my Squier VM on full, the noise I'd get when not touching the strings would be unbearable (almost as loud as the note even), so I tried something. I soldered the jack's sleeve (ground) terminal to the back of the tone pot with a nice sturdy thick wire. I still get that noise, but at a fraction of the volume. It should hold me over until I get my shielding kit and wage the ultimate campaign against noise.