but what is more important is that they had managed to keep the plane flying (arrested speed decay and made typical stall avoidance maneuver to gain the speed). With the vertical speed constantly increasing the higher the plane speed the better was the chance to glide to the ground instead of falling on it. And with higher speed the control movements had better chance of success.
This is exactly what I'm saying. Now you seems to be convinced that retracting flaps from 30 to 25 is a much higher priority than to stop the AP pulling on the nose...
On a constant path (ILS) a flap retraction requires an AOA increase, which is opposite to what is required to increase the speed (AOA reduction). Retracting flaps in order to reduce drag at constant AOA would require a steeper path and in order to increase the speed the AOA would need to be reduced. The speed didn't decayed because of the flaps but because the AP was constantly increasing the AOA. That's the first thing to stop in order to preserve energy. Flap retraction from 30 to 25 is only improving gliding efficiency once AOA and speed are under control.