Plugs are always a source of problems, direct wiring as it is done in CNC machines Etc is less work and less problems
Start with the filter and new cable, a shield would be very beneficial in your case as every thing is very compact
Some Ideas on how to Ground the Shields
Some VFD Drives already have built in Shield Ground clamps snips below
EMI Glands perform the best for through Cabinet mounting and Spindle mounting for Shield Grounding
So lots of snips for you to look at
Mactec54