@Filler Dent
"No trim tabs here. It's FBW."
The jackscrew is the trim mechanism.
On the idea of the huge variations in vertical speed without corresponding altitude changes: This is fairly easy to explain. (At least possibly)
After the tail separated the plane almost certainly tumbled numerous times. (This also explains the disintegration of the weakened rear fuselage up to the wing box- where it was strong enough to resist the continued failure of the fuselage skin...) As it tumbled roughly around the middle of the now altered CG the nose would have gone through a series of oscillations in quick form. Down at an extreme rate until the nose passed through the vertical facing downward, then up at a fantastic rate while the nose rotated up to the vertical again, before once again beginning the down cycle as it passed through the vertical.
Because the pitot static system is located in the front of the airplane (almost as far forward as it can) the readings would have been way out of whack, and would correspond at least generally to what was seen on the traces.
Finally: A flat spin: This almost certainly did not happen as there was nothing left to induce the adverse yaw necessary to initiate the autorotation required for such a spin. Further the impact shows pretty clearly that the wings were not rotating about the yaw axis in any meaningful way. If one engine failed and the other continued generating thrust it is at least theoretically possible that the airplane could have been forced into a spin, but given the weight and balance of the failed fuselage to that point it is incredibly unlikely that this happened.
Just my .02 as always,
dce