While I'm waiting for Zorin, I'd like to suggest a possible (sic) explanation for what we know.
I trust the Pilots were doing all they could. I trust they were highly qualified. I trust them easily as much or more than I do an a/c whose bread and butter is autoflight, and not UAS.
After the STALL, and what I take to be a proper and trained PF response, we find that the THS is 'held' in almost maximum NU. For this, the Pilot holds NU, well after his 'recovery' from STALL WARNING. What on Earth causes a Horizontal Stabiliser to be planted almost to the stops NUP, and in a STALL, with an extreme r/o/d?
Let alone a Pilot with full back stick? As I mentioned above, my opinion is NU stick is what gave the PF the best ND response.
Pardon? There is no other explanation except 'He didn't know about the Stall'. What else could this attitude be? Nose in the sky, tail first descent in average 10k fpm? No other attitude explains the basic environment, Panel or NO, Viz or NO, QRH or NO.
ACARS be damned, the trickle of 'data' from BEA aside, I think I know what explains this, if not the climb.
Also the "Duet" on ss at 10k.