"There is no wiggle room with a helicopter. They drop like a stone."
That's not actually correct. A helicopter that suffers an engine failure will "auto rotate" and, providing it is piloted properly and the transmission has not suffered damage to prevent it, the rotor will turn freely and provide sufficient lift to enable a controlled descent. Helicopters have a "freewheel" device which disconnects the rotor from the engine in the event of power failure or failure of the tail rotor. It's rather like a fixed-wing aircraft gliding after loss of engine power.
Of course a safe outcome depends on there being somewhere safe to land. The main causes of helicopter crashes are either seized transmission (which prevents auto-rotation) or landing under aut-rotation but in an unsuitable place.