This will not solve the GFCI issue, but i noticed something else.
In the schematics a LM358 or LF353 is used as driver for the Pilot signal.
I have not measured the outputs of these Opams yet, but according to the datasheet, they are not rail-to rail opamps.
So in theory the voltage swing might not be -12V to +12V but less then that.
This might give some connection problems, as the Car might not be able to sense it's connected to a EVSE.
My DIY EVSE is partly based on the
Roadster Foundry Mobile Charger
M. Eberhard used a LT1498, dual rail-to-rail opamp. So i decided to use the same ;-)
The EVSE i made also measures (with the pulses coming from a kWh meter) the other loads on the same phase, in my case i'm limited to 25A max. Any higher then that and my main fuse will blow.
So if for example the Oven and Microwave are on, the kWh meter will tell the EVSE to limit the max current for the roadster temporarily (by adjusting the width of the Pilot signal)