There's a very quick and dirty fix you can try to see if separating the ground wire out makes any difference.
Undo the little grub screw that holds the base plug in place (1.5mm allan key),
Ease the base plug out a little - careful, don't pull the wires inside. You can get maybe 5mm of clearance.
Unsolder the ground lead from the little brass tag. and strip it back a bit (really burn off some of the insulation with a soldering iron).
Put the ground wire on the outside of the base plug so that it contacts the metal base when the plug is put back.
Put the plug back in the same position, don't twist it round as it has been set so the wires don't pull as the arm rotates.
Wrap a ground wire round it and secure it with the locking nut.
If this makes a difference it's worth doing a more permanent, soldered ground.
All rewire kits just supply the 4 cartridge leads.