FE Hoppy:
Well the pitch input was at 05 and the climb commenced at 16. The peak value was 7000fpm but the mean was about 1400fpm. If we are to believe the the quoted speeds they lost 60kts in this manoeuvre and ended with the same thrust setting and 4°alpha.
How about this scenario:
PF makes his correction for roll and doesn't notice the rate of climb or is confused by the stall warning. When he notices the 7000fpm he corrects with nose down and levels at 375 all without adding thrust. He's now at 4°alpha but having not added thrust his speed is reducing which induces the second stall warning. Now he adds the thrust and pulls up. The aircraft doesn't have much more thrust to give and his alpha is increasing all the time while the speed is reducing. We know that the isis speed comes back at 2:11:06 (15 seconds later ) and shows 185 which matches the PFD.
There's no reason to think the climb didn't start shortly after the nose up input just after 05. A big weakness of the narrative format that the BEA adopted for this report is that it makes it hard to tell when the events being described are basically simultaneous and when they are sequential, and you really have to be alert to subtle tense differences (eg TOGA was set at 2:10:51, but the throttles are already at idle at 2:12:02, so we don't know when in the intervening period power was reduced).
Other than that, your scenario is not implausible. And could it be that they attributed to turbulence the upward acceleration that they must have felt?
So this puts us at the top of the climb, at the edge of the stall (or at its beginning). What is much harder to understand, though, is the following three-some minutes. Other than power being reduced sometime before 2:12:02 and some nose-down inputs at 2:12:02+15, there seems to have been little effort to break the stall. What was going on in that cockpit?