Matt, you have to remember that the Electra probably would not have floated the same way that the Airbus that "Sully" landed in the river did.
His fuel tanks were in the wings and "belly" of the aircraft. The cabin and a good part of the wings were above at least a good part of the flotation that was available for the Airbus.
The only tanks in the Electra that were below the cabin were those in the wings and they would not have prevented the ship from sinking. Sea water, and quite a bit I would guess, would have had to enter the cabin of the electra before enough flotation would be provided by the internal tanks to prevent the aircraft from sinking. Most estimates that I have seen think that the nose of the airaraft would have settled more than the rest of the cabin which would most likely mean more water up front. Up front was where the radio receiver, located under the copilot's seat, one of the batteries (the only access to which was through an outside hatch in the belly of the aircraft) and the dynamotor, located under the pilot's seat, that provided the AC electrical power for both radios were located. The transmitter and the second battery were both mounted on the floor of the aircraft near the navigator's station in the rear of the aircraft. They might have also been in the water, but if not, the items up front and most of the electrical wiring would probably have been quickly shorted out by the water.
Moving the battery and radios would not have been enough to make them work. The electrical wiring would have had to have been moved too. AE couldn't make the RDF work. Do you really think she could have rewired the electrical system? I don't think Fred could have done it either.
Below is one of the Harney drawings that shows where everything was located. Maybe that will give you abetter understanding of the problems.