Well I don't know what to suggest really. When you say squirt water under cam cover do you mean louvred cover down centre of head (coilpacks are under) or one of the actual cam covers???
If the first case is true maybe you have some dead coils, who knows.
First thing I would do is ditch the "dodgy" ITC and put it all back to factory. 1JZGTE's are notoriously reliable and part of the reason for this is the true distributorless system amongst other things.
I would bet considerable money that the problem is something thats been done to the motor.