The tail rotor wasn't failed, it was sub minimum pitch. So even if you snapped the collective down it would continue to spin left (the tail rotor is driving the thing left rather than the yaw being a function of the torque reaction). So even with the lever full down and cyclic stuffed forward, you wouldn't gain much airspeed as you're yawing hard left despite the lever being down.
Of note the minimum position of the tail rotor is determined in design by some flight condition where left yaw is required at very low power. On several types I've operated this was defined (and tested during a maintenance test flight) as the ability to yaw left at a reasonable rate (cannot recall the exact condition) whilst in a zero speed autorotation (great fun to do that flight test). In this incident the yaw setting was even less than this due to the mode of failure. That's a lot of yaw and even by day at several thousand feet I would suggest you would struggle. I would expect the required recovery action would be to lower the lever, pitch hard nose down and roll - I think roll to oppose the yaw (and also further reducing power/torque requirements) so you could accelerate but rolling into the yaw might offer the chance to align the fuselage with the airflow. Pure speculation as you could never test it.
Those guys had a awful roll of the dice that night.