Owain: wow.
Here is a summary of what I gleaned from your post. Please let me know what I have misunderstood.
Once stalled at altitude, and with CG as estimated, (be it 29% or 37%) the center of lift of the wings will provide a
self-correcting nose down pitching moment proportional to such lift as the wing is still creating.
Per the FBD I just sketched on my napkin, the arm that the force acts through is of the length somewhere between 70-29 to 70-37, (as outer boundaries). Based on where the THS is, I'd guess its relative number for arm calculation is about 96 or 97. (Am I close?) as compared to the center of pressure on the wing. (@takata: thanks for the posted CoG chart).
Thought: IF THS and elevator (as a lift producing system) have lost control authority or were stalled, THEN there would initially be no force from the back end, or a very small force, countering the "self correcting" pitch down moment of the stalled wing.
Thought number 1:
As the nose attitude gets closer to level, wouldn't the C of P start to move forward from 70 towards a smaller value, and gradually reduce the length of the arm, and thus the moment, of the correcting tendency?
Thought number 2:
THS is an airfoil, so even if stalled, it produces some amount of lift and thus provides, through that longer arm, some counter to the correcting tendency of the wing whether or not it is stalled.
Your line of thought presents me with the provisional conclusion that the THS was not stalled, since the nose stayed up (per the BEA report) and didn't (as far as we know) oscillate up and down as it might if the THS were stalled.
What you described is a "natural" pitching down movement (??) of the stalled wing, which seems to have been countered by the longer arm being acted on by lift from an unstalled tail/THS.
Am I close?
If that's about right, it leaves me with a non trivial concern:
if the nose stayed up due an input or command other than pilot control inputs, the nose being held up by (THS lift) x (arm) prevented stall recovery for about 30 thousand feet worth of travel down to the surface.
As Retired F4 points out, "We don't know." In this case, ignorance is surely not bliss.
The above sort of reasserts a fairly obvious point: an ounce of stall prevention avoids about 200 tons of attempted cure.
From PJ2's linked article on high altitude handling:
3 Maneuvering Stability
An additional effect is that for a given attitude change, the change in rate of climb is proportional to the true airspeed. Thus, for an attitude change for 500 ft per minute (fpm) at 290 knots indicated air speed (kias) at sea level, the same change in attitude at 290 kias (490 knots true air speed) at 35,000 ft would be almost 900 fpm. This characteristic is essentially true for small attitude changes, such as the kind used to hold altitude. It is also why smooth and small control inputs are required at high altitude, particularly when disconnecting the autopilot.