I view the learning curve of flying an AOA as similar to learning what
circumstances sets off the smoke detector in one's house.  We learn a
conditioned response of what to do when it goes off.  Just as importantly
... we learn what is going to set up the circumstances to trigger an AOA
warning ... if those parameters are exceeded we know something other than
stable flight is going to happen.  The AOA warning device does it's watch
dog job by watching ALL the parameters leading up to exceeding an angle of
attack which would cause the wing lift to decay.  The senses of a pilot will
eventually learn the parameters but will never consistently predict critical
angle of attack with the infinite number of possibilities which could be
created.

> recognize the impending stall early (helped by the AOA), level the
> wings, and push the stick forward with power.

Good training addresses unloading the wing first while advancing thrust to
avoid a stall.  Get that airfoil flying with smooth air flowing ... then
.... level the wings.

2 cents worth of opinion  ....
Jerry Grimmonpré