I would not bet a lot on maintaining the ILS path as the flying crew priority
Anyhow, following sequence was used:
1. push the throttles fully up, wait for results
2. repeat push the throttles up, wait for results
3. reduce flaps, wait for results
4. push the nose down, steer to land
Obviously after the second unsuccessful attempt of thrust increase something else had to be done to save speed. Retracting flaps on the ILS is not increasing/saving speed, on the contrary, maintaining the ILS (which btw leads far beyond the threshold) is actually the only reason that caused the speed to decay.
When you fly a glider, speed is not constantly decreasing because of the lack of engine or because of a wrong flap setting. Speed only decreases if you increase the AOA, ie when trying to follow an unachievable flight path.
When the crew detects speed deviation it first acts on the thrust. If this is unsuccessful, there is only one way to save/increase speed: acting on the AOA/flight path. As such, without available thrust, AP disconnection and AOA control is the number one priority, acting on the flaps while the AP keeps increasing the AOA is totally irrelevant. While I understand such a wrong sequence can happen with short reactions delays, I'm really surprised that you can't get it after a couple of days of discussions behind a computer.