I'm reluctant to trawl back through this long thread for references, so please forgive the lack of detail.
My recollection is that when the second engine runs down, the generator drops out and there is no facility to transmit from the Police radios on board. Nor would there be time to get a radio out of where it is stowed.
Secondly, and I am on tiptoe here, all the talk of voice recorders overlooks the fact that if only some people know that things are wrong, only some people can talk about it.
In this particular incident, then a voice track would establish if the crew discussed the fuel state at any stage of the flight. A good series of data tracks would record the time that various events occurred and were presented to the crew.
None of which would necessarily explain why a serviceable aircraft, apart from thrust, failed to end up in the river, on floats.
I point you back to the Dyfedd Powys incident. A proper briefing by an experienced ex military captain, keeping his crew informed and when, from only 400 feet, both engines quit, they shout for help on the way down and all walk away from the aircraft.
Tigerfish, I am surprised at your input here, Sir.
We might never know, we all need to get over that.