So I asked myself: how does one recover from a stall without reliable airspeed and without AoA?
This is simple stuff, you use your remaining instruments and return to basics: use pitch and power. And you certainly do not continue pulling.
I would think that the proper action would be a determined nose-down push, maintained until the stall warning stops, and then trying to maintain an AoA on the edge of s/w, gently allowing the nose to raise until s/w occurs, then a small nose-down correction to silence it, etc., until back in approximately level flight at a reasonable pitch attitude.
Scary stuff,. You don't use the stall warning to calibrate your response, you use your remaining instruments and your knowledge of your aircrafts pitch/power settings. Your solution puts you at an unnacceptable risk of secondary stall and that is another opportunity to enter a spin. If you do not know your aircraft's pitch/power settings for level flight then you are not competent to pilot it/manage its autopilot and take over if/when that autopilot fails.
EDIT:: Can anyone be expected to do that succesfully without being trained for that eventuality?
Of course not, you are not born with the ability to recover from unusual attitudes using partial panel. You learn this when you take your instrument rating. If you have lost your scan you are not competent to fly in clouds.
It really is that simple.
I'm struck by the fact these guys managed to "fly" and reverse course at what is essentially under minimum controllable airspeed, for five minutes, in turbulence, and they hit the water belly side down and reasonably flat. That is a huge credit to the designers of the airframe, must be inherently incredibly stable.