Fair point, but there's an important distinction between "all the while", as you put it, and the actual English translation which is:
But I’ve been at maxi nose-up for a while
(Final report Annexe 1 - p31)
"All the while" would imply that he's been pulling full stick back since the onset of AP disconnect, which does not tally with the DFDR trace. "For a while" implies that he has been consciously doing it for a period of time, but gives no clue as to when that period of time began.
Towards the end of the sequence, as the aircraft was descending in a mushy stall, it's fairly straightforward to reason why he may have decided to pull up. But at the beginning of the sequence, when the aircraft was still flying and the two F/Os had just discussed why they could not safely climb higher, it becomes a much more problematic issue to fathom out.