I am very happy to share a solution to the ground hum problem the esonic2 p/u system. My AJ500ME was working fine until I stuck my hands in it to give the input jack more threads sticking out to accomodate the strap button. While I had the strings loose I removed the shim under the bridge to lower the action which was required after I eased the truss rod to correct a dip in the neck at the first five frets. With the strings back on I had a new best friend.
Then the ground hum demon appeared. Just like some have posted the hum was not there until the strings were tensioned almost to full pressure, pointing to a short in the under bridge pu. I filed the sharp bend of the entry hole, as mentioned earlier in the thread, to lessen the potential pressure on the pu wire and it seemed better but was just a different type of hum. It also was affected by touching the input jack, the bridge,touching an amp screw, and even standing or sitting on a stool. This was now a full scale war now that I had a mistress to save from true evil.
In my many mirror searches I had noticed the half twist(only overlapped once)in the wires held by the notched pegs just above the sound hole. This reminded me of twisted phone wires to prevent electromagnetic interference and I was encouraged by a friend in the marine aftermarket who just had a meeting about this very situation. I carefully removed the two wires from the pegs, just inside and above the sound hole, and twisted the braided wire gently around the larger black wire as much as allowed. Only the large black wire had to be put back in the notched peg as the wire braided line was held by the tension of the wrap. My baby is now singing without unwanted accompanyment, the hum is gone.
Sorry for the long story but surely you guys understand the need to share true bliss. I'll be calling the 8004gibson help line back to hopefully get this solution to the assembly line. The guy I talked to earlier in the week is waiting to see if replacing the shim I had removed solved the hum. I'll be happy to return the good deed they did in sending me the strap button that missed the bus. The strap button came connected to a complete input jack assembly. Gibson customer service seems more than alive and well to me.
The blended pickups do give this guitar a unique voice and I hope this fix gets out to all who are thinking they have a lemon.
Shine the light,