I don't think you should aim to install an additional permanent earth until you discover what (if anything) solves or improves your problem.
Out of desperation, my approach was to have an additional flying earth lead with a bare end and start grounding various parts of the system to see if I could make an improvement. I soon found that the only places that helped were on the empeg itself, not the sled nor the sled wiring.
For me, the best result was at pin-5 (GND) on the serial connector - silence! It was impracticle to implement this permanently but I found that the outer shroud on the AC RCAs were a 2nd best. To achieve an installed fix I used a short strip of metallised foam gasket stuck inside the sled at the rear - when the empeg is docked the RCA shrouds ground against the mesh. This gasket material is often used to provide RFI shielding in electronic enclosures - I robbed my piece from an old PC