You always hear about "Grado hum" and unshielded TT motors are a problem.
But you describe static, not AC hum.
ISTM that what you have is the need to change the grounding set-up of table, cartridge and arm.
Is the table grounded or are you only using the ground on the cables?
Add a ground from table chassis to either the phono ground or another component.The beatings will continue until morale improves