“...a well-known deficiency in the F-14’s Pratt & Whitney engine....”
P&W probably got more than a few memos on that “glitch”.
Although I know nothing about the aircraft, as a retired pilot with many years experience in prop driven aircraft, I doubt that the engine is to blame.
All sorts of weird changes in airflow occur when high performance aircraft change angle of attack or similar changes in attitude.
My suspicion in this case would be that the “slight” course correction caused a disturbance in the airflow to the engine.
For instance a slight skid or sidslip might have caused the fuselage to disturb the airflow, thus causing the engine to lose power.
Only a person highly qualified in that aircraft can answer this question, and I am not that person...but I do know that it is possible.