Oddly when the Ebers-Moll enters the discussion it is with no explanation and is just to impress the readers so let us look at the model.
Some food for thought,eh?
EDIT: I should point out the power handling ability of the transistor will need to be watched if using the circuit. The question would be ,'what is the base current?' Using a higher base current could burn the base out. It might be worth a test board.
EDIT 2: I think a 2N5550 will work backwards too.
Another circuit to test.