The initial storm climb
Although not an airline pilot, I have read every post on this thread. There are a couple of things as yet unexplained:
1) there seems to be an assumption that the first (2) stall warnings (just after 2h 10m 05) were spurious, possibly related to the IAS error. Firstly, there is nothing in the BEA statement to suggest they were spurious; and secondly, as the stall warner is fed from the AOA indicators and not the pitots, the IAS error would surely not cause a stall warning
2) the "storm climb" at 7000fpm for 2500 feet is not explained. The PF made "a left nose-up input" not, as he is later stated to be making, "sustained" nose-up input. And there is nothing in the text to suggest that he pitched the aircraft up to the extent needed to climb at this rate on cruise power settings - surely that would have required 20-30 degree pitch angles that would surely have been mentioned? There is also a mention of nose-down inputs in this phase
On the other hand, a big updraft would both lift the aircraft without big pitch-up, and cause the AOA to increase, perhaps setting off the stall warner?
Where this leaves the explanation of the crash I don't know, but we do not yet seem to have satisfactorily explained this first 45 seconds.