PJ - having never handled a side-stick I have no idea what a 'normal' manual input would be to maintain level flight, but 3-4 cm seems excessive to me, and certainly 6" on a Boeing yoke would raise my eyebrows as PNF. Would you expect that as a 'corrective' input?
I disagree on the 200t being immaterial - you speak of momentum - yes, 200t of it to get moving upwards. It does not matter what the steady state S&L match is, you still have to start the elephant moving upwards from his seat!
The more times I read the interim, the more unlikely the whole scenario becomes - at some indeterminate time after 2:10:16 a climb begins. The next 'fix' we have is at :51 with a stall warning AFTER the climb has been 'killed', so we assume that around 30 seconds or less of 7000fpm happened (probably about right for the height gain) during which NOSE_DOWN inputs are the only ones mentioned. So, the a/c must have pitched fairly rapidly to climb pitch to do what it did (and equally 'fallen out' or bunted over equally rapidly at the top) and can we assume then that it was pitching nose-down in response to the elevator input for several seconds?. Do we have any idea of the 'g' required for this pitch up into the climb? I see 1.75g quoted as an over-speed FCS 'increase' in applied PF input. Are we close?