There is no problem going below best auto airspeed, especially if it means keeping the rotor RPM in the green range. Autorotations can be done at a great variety of airspeeds, including if necessary zero airspeed (not recommended, but far better to be at zero airspeed with lots of rotor RPM than to be at airspeed with no or low rotor RPM).
Pushing forward on the cyclic automatically following an engine failure was the subject of a superb article in one of the newer magazines recently - basically - don't do it.
There are people who do autorotations to holes in the jungle and then drop at zero airspeed into the hole and survive the landing at the bottom (they even train for this). So there are lots of ways to do this, but the key is that you have to have rotor RPM - not necessarily airspeed.