Use a separate earth ground for the table and plasma unit. A ground rod close to the table with separate stranded heavy wire (10ga or bigger) from the plasma chassis to the rod and from the table to the rod.
Make sure the controller with the drives and electronics is NOT grounded to the table ground.
If you have to, drive a separate ground rod close to the PC and electronics and ground the PC and interface electronics to that ground.
If you have switches (table, home, e-stop) out on the table the inputs to the PC need to be opto isolated. The drive side of the opto's (inputs) need voltage to operate. That voltage needs to be from a separate DC source and should not be referenced (ground/return) to the PC ground.
If you STILL can't get rid of the noise you will need to use an AC isolation transformer for the PC/controller side and re-establish a clean local ground with a separate ground rod away from the table ground rod (3 meters min).
The source of most interference is conducted (through conductors) rather than through the air. Some of the older HF start machines will kill small animals with their RFI which is largely radiated noise (throught the air). Shielding and metal cabinets will go a long ways in reducing radiated noise but if you get the "clean" ground mixed with the "dirty" ground you will get noise that shielding won't help.
HF noise elimination is a lot different that grounding for safety at 50/60HZ. Any unbalanced line of more than a few inches becomes a potential antenna!
Do you have the port signals from the PC buffered to the drives? PC ports are basically high impedance I/O. Having the signals being driven from a power buffer into a low impedance load keeps radiated noise (and a lot of conducted noise) from getting back into the low level logic and causing the false step and dir signals you are seeing.