I think the cavitation found in the pumps is probably misleading the line of thought of everyone in this forum. IMHO cavitation could have happened prior to the event in question, like a couple of days (or the sector) before. So leaving the cavitation signs aside:
If the fuel metering device was giving a “false” reading, somewhat bellow true fuel flow, when the A/T commanded an increase of thrust it would have increased initially to the requested value but then the excess of fuel in the burners would made it drop dramatically but not entirely. Thrust decays, FADEC opens fuel valves even further to compensate, but instead of correcting it worsens the problem.
Too far off the mark?
GD&L