Kiwiguy
You are making a bold statement that Quote,"On ETOPS flights APUs must be run continuously", it might have to be on your fleet type, but as a whole you are incorrect.
I do not know of any aircraft that was designed for ETOPS operations that has to have an APU running continuously while in the ETOPS stages of flight.
The only time that you do have to keep it running is if you have a generator inop.