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.
Yes that is right
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).
I may have misunderstood your numbers, but no, The CG and CoP numbers are % of mean aerodynamic chord, which is about 7.3m. The tail arm, from 37% mac back to the usual reference point of 25% tail mac is just under 29m, so the relative number for calculation is around 400.
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.
Not sure what you mean by lost control authority, but if THS and elevator were stalled there would still be a substantial force at the back end, either up or down depending on which way the THS stalled, but it could only be decreased from whatever value it had before the stall.
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?
Yes it would, but of course the aeroplane would be moving back towards the unstalled state and the tail would still be giving substantial ND moments, which greatly outweigh the wing contribution.
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.
Yes, as noted earlier
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.
Yes again.
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?
Yes
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.
That implies an input or command other than pilot control inputs. As I said in that earlier posting,
without significant and continued up elevator application, even with the THS at -13 deg, you won't get any nose up pitch from the back end above about 26 deg AoA. Well maybe I didn't actually SAY that, but it is implicit in my argument. 26 deg is more than enough to stall the aeroplane of course, but AF447 has been linked to much larger values of AoA that, IMHO, can only be achieved with up elevator. I will leave it to others to argue whence came that up elevator.
The above sort of reasserts a fairly obvious point: an ounce of stall prevention avoids about 200 tons of attempted cure.
Who could deny that!