It wasn't an overbooked flight.
It was a full and boarded flight that needed to accommodate 4 DH crew.
The operator needed to do the following:
Make an announcement explaining the situation
State clearly that the flight would NOT operate without the DH crew being on board.
Ask for volunteers
If not enough pax step forward, deplane EVERYONE.
Separate the unlucky 4 from the rest of the passengers and board the remainder
End of story