It's the RFI from the drive and associated wiring more than the presence of 480 V that is causing the problem, I'm guessing.
The 4-20 mA circuit should be twisted, shielded pair - sounds like it already is.
Is this 4-20 mA cable in the VFD enclosure itself? Does it run in its own conduit from there, or is it running with the drive ouput to the motor?