Adding grounding (in a way to satisfy (edit: was 'CCID GMI') ICCB grounding-monitor) is bonding, and I defer to Oilpan4's experience. I guess one can use an isolation transformer, as GerryAZ is thinking, and bond its output to provide grounded and grounding conductors. But that is another inefficiency, and it does not add real safety.
Having protective Earth, equipment grounding conductors, increases safety of permanent building wiring. Original Poster's inverter's output is floating; it is not grounded/bonded to mass Earth. Nissan's portable EV supply cord is meant to be connected to a built-in, grounded, electricity supply outlet. (Whether part of a building, or a pole in a lot, a permanent outlet _built_ to a place.) Its GMI feature is not useful in OP's situation.
2020-09-29: This post was edited to replace a mistaken term. I used 'CCID', standing for 'Charge Circuit Interrupting Device', which basically refers to a RCD/GFI/GFCI applied to an EVSE. Corrected term is 'ICCB', In-Cable Control Box. Or alternatively 'IC-CPD', In Cable Control and Protecting Device.
And edited: to tout a cheap adjustable EVSE which I would like somebody to put to use.