It's not the 60 cycle hum I'm referring to, it's crackling and popping from static electricity.
My Classic has '57 Classic pups.
I went to my local shop today to show my guitar to the tech. He was blown away and never heard of it before. Then we tested a few Gibsons in the shop: a Les Paul Standard, a Les Paul Studio, an Explorer, and a SG... through two different amps.
All 4 of the guitars had the same static issues as mine! They were not quite as bad, but they still had it. The tech (and a couple of customers) were shocked (excuse the pun) that they had never heard this before.
So at this point I'm going to pull everything apart, add copper shielding and ground to that. I'm in the middle of a very intense course for work, so it will be a couple of weeks before I can get at it.
It's pretty sad that I have to finish the production of a 2300 dollar guitar. Without messing with it (like I will have to), it seems the only solution to the problem is to buy a PRS...