Speculating
Correct me if I'm wrong, but there are only two ways that the Airbus could have climbed as rapidly as it did: with severe and persistent up elevator or with CG way too aft. We have reports that the CG was well within limits. So that leaves severe and persistent up elevator - something that should not be allowed by the FACs. So we have a problem with either the FACs or the elevator itself. It is reported that both FACs were reporting a fault and that the stall warning was sounding. So it would appear that the FACs "knew" something was wrong and that the plane was in a stall. From this thread, it is reported that the FACs respond to a stall condition by increasing thrust and applying down elevator. It is possible that the FAC software failed in this simple duty, but I would bet against that. Also, if the main problem was with the FACs, then cutting them out should have made the flight recoverable by ATC pilots.
That leaves the elevator itself. If the pilot started a climb, the elevator may have visited a severe up position. If the elevator got stuck in that position, the FACs would signal a fault and the plane would attempt an inside loop and enter a dramatic stall.
But why would the pilots take out the FACs that were already trying to get the elevators into a nose down position? So that they could do something that the FACs were not programmed to do - attempt to shake the rudder free.
Please feel free to poke holes in this notion. That's what I've posted it for.