Welcome to the unfair reality of analog, Mark. I had this battle with my system about two years ago. First off are you using a phono stage? If so try alternate grounding on it as well. Also try grounding the turntable to a different ground on a differnt circuit. Also I ask, does the pitch or tone of the hum change when you connect the ground. Turntables are natural receptors for EFI as well as RFI. Are ther an reostadts(e.g. dimmers) on the same circuit, Do you have a halogen light nearby, or a radio broadcast tower? Sometimes with RFI just changing the position of the turntable or proximity to the rest of your system can change the amount of hum. Another source could be your system, some CD palyers generate a EFI, try turning off the cd and see if you get a change. Mark all I can do is advise you try these things if all fails try a power conditioner/cleaner e.g. PS Audio, Monster etc.
Good Luck
Good Luck