How does the engine produce aerodynamic lift at high angle of attack?
Anything, even a metal plate creates "lift" when it is under an angle with an air flow. Lift isn't a magical attribute to "wings", it is just a physical consequence of the law of conservation of momentum: when you push a stream of air down, the reactive force is upwards.

the fuselage/engines also act as minor lifting surfaces: when they are under an angle they, inefficiently, redirect the airflow downwards. 

For the engine this is also a bit due to the definition of thrust: thrust equations consider an inlet in the same direction of the thrust vector. So the inlet &amp; compressor redirect the flow "downwards" under high angles of attack. - This effect has to show up somewhere: as a lift force generated by the engine.