how on earth can I earth the player to get rid of it
First thing is to try earthing the 12v supply. Connect the negative terminal of the 12v input of the inverter to a metal water pipe, the earth pin of a GPO or some other object known to be earthed.
If the turntable is constructed on a steel chassis then try earthing that.
I know that some US made record players did not isolate the shield of the pickup cable so I'm not going to say go and earth that directly, though you could try doing so via a .01uF capacitor. Taking this a bit further, you can also try earthing the amplifier chassis via .01uF capacitor. Earthing via a capacitor like that will still allow the chassis to be live, but yet earth it at higher frequencies.
