If I understand the system, there are multiple requirements which, when combined, are mutually inconsistent. Something in the design or requirements needs to change to achieve the customer's desired functionality.
The requirements are:
1) use a VFD to control some chemical application
2) use a cord and plug connection to permit the system to be interchanged with other hardware or to other locations.
3) have the equipment operate at 110V at the receptacle
4) comply with the NEC, which brings in a GFCI requirement.
IMHO you can change one of the following:
1) You could use something other than a VFD to control the process. Ingenieur has been posting several concepts, but I doubt you want to get into re-engineering the application system.
2) You could do something to decrease the leakage current. The PWM switching frequency capacitively couples to the motor frame which causes _expected_ leakage current to flow. Decreasing the switching frequency would reduce this current. Insulating the motor frame is a possibility, but this would _create_ a shock hazard (limited and expected leakage current coupled to the egc is safe, an insulated frame blocking this current means that you get a shock when you touch the frame.) Perhaps filtering between the VFD and the motor could reduce the leakage current. Perhaps get the motor rewound with heavier internal insulation to reduce capacitance.
3) You could change the setup to remove the GFCI requirement, eg. using 480V cord and plug connections, with a 480V input VFD.
4) If this is really a low power system, perhaps you can operate at much _lower_ voltage, eg. a VFD with a 48V DC bus and motor rewound to match.
5) The _receptacle_ has a GFCI requirement, but does the equipment? Could a 120:240V step up transformer be made part of the equipment, with no GFCI on the _hard wired_ connection between the transformer secondary and the VFD?
Something has to give; the question is: what is the easiest/cheapest thing to change.
-Jon