retiredF4:
IMHO Elevator ND or trimming the THS down, after this high AOA of 60° was established, only increased the drag of the tailplane but had no permanent effect to get the nose down to the horizon and to increase the speed as necessary.
It has to be noted that at an AoA of 61° Drag along the Flight path equates to Lift by Factor ,87. So if your tail creates 1000N of Drag along the Flight Path that will eqaute to 870N of lift. Therefore increasing drag on the Tailplane is a good thing. Adding ND elevator will increase camber which again will increase drag and remaining lift.
As has been pointed out lift above the stall decreases bút it doesn't drop to zero.
Slight excursion:
I highly appreciate the fascinating insights of @gums regarding the stall behaviour of the F-16 but it has to be noted that the two designs are very different. In an F-16 much of the lift post stall comes from the strakes (they produce vortex lift which is not susceptible to stall as opposed to traditional wing lift). They are mounted forward of the wing, thereby shifting the CoL forward post stall. That was one of the main reasons for the rather agressive (meaning restrictive, being between 15 and 25°) AoA limitation on the F-16 compared to more conventional designs like F-15 and F-14. High AoA shifts CoL forward on the F-16 therby further increasing longitudinal instability.
/Excursion end
The fact that the Stall warning came back after some Nose Down Input due to the IAS exceeding 60kts again also points to the fact that the control authority was not really lost.
The problem is that reaction probably was quite slow.
So in the heat of the moment it might have appeared as ineffective even if it wasn't.
When GA planes spin it sometimes takes multiple revolutions with opposite rudder to stop it. It is surely not easy to resist the urge to try something else. However those who follow the urge often pay the ultimate price.
On the other hand we still have no clear information if the pilots in this case ever realised their real situation and Flight Path being deeply in a stall. Reading the scarce information we have I have the nagging feeling they didn't.