I've been struggling with a les paul trying to keep it quiet after shielding the cavities and all. In the 80's gibson was shielding the control cavities with some nice plates and copper tubes in the jack plate cavity. They stopped doing this?
Anyways, after shielding, I still had noise coming through the guitar. The thing I noticed is if I moved my hand in front of the jack or covered the jack completely with my hand it was dead quiet. I even used shielded cable that hoffman sells here from jack to pickup switch. I removed the jack completely and wired straight to the amp. That was dead quite. The normal switchcraft jack acts like a huge antenna the way it's designed.
Pick up one of these from hoffman.

And enjoy the silence. Works perfectly for shielding without trying to shield the jack route with copper tape that's just a pain in the ass trying do in a jack cavity. You can even add a male jack cover to the end to shield the connection if needed. The majority of the noise is from the original jack. Not needed in a strat, sg or flying v since when you shield the control cavity on those, the jack is encased inside the shielding. But for those les paul type jack routes, that end pin jack is a gift from heaven. I literally have to press my les paul against a noise maker radiating emi to get any noise and when I do that, the noise is very minimal. I can't believe how quiet it is now.

Thought I pass it on since I remember some one else going through this same issue.