Jolly Tall
I was taught almost the same as you except for one notable exception, which was raised by John Farley and relates to the application of rudder before elevator.
Imagine an aeroplane in a spinning attitude and take a mental snapshot of it from the side. Mines a C152, nose down pretty convincingly (about 45deg in my mind) and yawing and rolling and my one is stabilised in pitch cause I'm not smart enough to imagine too much.
The relative airflow superimposed onto the picture is about 10deg forward of vertical, going up. Now zoom in on the tail section.
With the c/c forward, the elevator blankets the airflow from reaching most of the rudder, only a little bit right at the bottom is actually effective to stop the rotation of the spin. This as we know is an important part of the recovery as we need to get the RAF straight on to the airframe as much as possible.
If however you hold the c/c back, the elevator is up. This allows the air to cover a greater portion of the rudder, so it is more effective and we can stop the rotation quicker, therefore recovering quicker.
I remember trying this in the C152 I was doing my aerobatics rating in and either way it tended to recover pretty well straight away, although there was about a quarter turn more if I did elevator first. The manual for the C152 says full opposite rudder, PAUSE (it is actually emphasised in the book), THEN check forward.
Then I started flying the Tiger Moth, tried the same thing, with an instructor of course, and it didn't stop within another 3/4 of turn
so I hauled the stick back to uncover the rudder and hey presto, the rotation stopped 1/4 turn later, check forward and away we go again. The flight manual says
Section Three: Emergency Procedures.
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So you figure out how to best recover in the type you are in, or you don't bother learning from your own mistakes and you learn from ours or others'. Note, the principles described above apply to aircraft with low tailpanes/elevators, not to Traumahawks, Seminoles (you weren't actually spinning them were you JF?, just stalling?) or Galaxies, BAe146s etc. Although they would be spectacular to watch. From a distance.
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Confident, cocky, lazy, dead.