So a few things --
(1) Search this forum for hum and noise threads -- I know this topic has been discussed in extensive detail over the years, so you'll find lots of approaches to analysis, and lots of fixes
(2) As I said before, if the noise goes away when you touch the strings, then your instrument's ground wiring is fine -- and so is your jack. And in a sense you're right that YOU are the source of the noise -- as we all are. What happens is that your body acts like a big antenna, collecting noise, and keeping drawing it near your instrument. A PC monitor may be worse, but you still bring quite a bit of noise right near the electronics cavity of your bass. When you touch the strings, what happens is that you create a path between the noise you are collecting and the ground lug on your jack (by way of the ground wire between the circuitry and the bridge). So touching the strings shunts that noise to ground (and thus AWAY from the circuitry that goes to the amp and gets amplified), and everything gets quiet. And that's also how you know your ground wiring is not the culprit.
(3) if the noise is the same when you restore the original circuitry, you can feel pretty good that you didn't cause it by modding the circuitry. And that's when I'd say it's worth looking into the shielding process.
(4) I could see how turning your tone down would reduce the noise -- since that drains some of the same frequencies. If you take an amp and crank the treble and drop the bass and mid, you would probably notice a hiss there too, but nothing that would indicate a problem.
I keep forgetting to ask -- do you get the noise when you have both pickups on full? Part of your analysis should be whether the noise is the same with each pickup on by itself, both on, each on full with the other on at 50%, etc. To make sure it's not just ONE of your pickups that's going haywire...
Keep us posted!