I haven't read of anyone trying it. In theory, something along this line can work.
A couple of challenges - some versions of the OEM EVSE apparently can handle 240V, some of them can't. (None are rated for it.)
Also, You'll want to make sure the pilot signal matches the actual current available, so the car doesn't pull too much power. It actually sounds like this might happen to work out for you - the OEM EVSE pilot limits at 12A, which is where it seems like you'd want it.
A couple of challenges - some versions of the OEM EVSE apparently can handle 240V, some of them can't. (None are rated for it.)
Also, You'll want to make sure the pilot signal matches the actual current available, so the car doesn't pull too much power. It actually sounds like this might happen to work out for you - the OEM EVSE pilot limits at 12A, which is where it seems like you'd want it.