If the problem were that the elements had become hygroscopic, then as they heated up (while the stat was closed) the water would be driven out, and consequently there should be no fault when the thermostat opened again (which we now know is not true). At the same time, if it was a problem with the elements passing current to earth, then the problem would exist if the thermostat was open or closed.
I am therefore beginning to think that there is some other fault. Could the thermostat itself have a fault in that it has earth leakage when in the open position? Is there some other circuit that becomes active when the thermostat switches off? Maybe an indicator light
In the first instance I would be tempted to conduct an experiment replacing the thermostat with a normal switch (taking all safety precautions including making absolutely sure that the oven did not overheat!!!) This would either identify or eliminate the thermostat as the source of the problem.
On re-reading this I think I should clarify that the experiment should only be for a few minutes. I did not mean this as a permanent or even semi permanent solution!!!