WilyFlier:
Once flaps are down Centre of Pressure moves aft, there is a requirement for a strong down force from tail trim and /or elevators. Loss of this down force is far more significant than pitch up from engines particularly if they are still winding up
The pitch moment due to the flaps will depend on the CofG relative to the Center of Pressure. If the CofG is aft of the CofP then the pitch movement will be up, however, (and as I continue to assert will be the case with the tail torn off), if the CofG is forward of the CofP, then this will produce a significant pitch down movement. That, combined with the complete elimination of any pitch authority due to the loss of the tail, would doom the aircraft more than certainly.
-GY