So it will start and run only with a lot of throttle then? Seeing as how the ignition components have been replaced and the problem remains, I would lean toward the fuel system. Maybe it's too much as Lance suggests, or maybe it's not delivering any fuel at all until the airflow is up to a certain threshold and that's why it won't idle below 3K RPM.
IIRC = "If I remember correctly..."
My '80 320i did start without the ECU connected...