That does make sense to me I just had a hard time getting it in my head that we spin as quickly as we do but like you said the pedals are not at zero pitch when they are centered so there is the extra force that spins us faster than what I would have imagined
I should probably leave AC to add the final word since he made the argument so clearly, but I just wanted to check you'd got his point.
The 'extra force' that made you spin sharply to the left as you slowed down too much is nothing to do with the position of the pedals, that has been constant throughout. What made you spin left so sharply is the sudden disappearance of some forces that were keeping you more or less pointing in the right direction when you were moving faster. Those forces include (but are not limited to) the aerodynamic thrust from the fixed tail fin, and the airflow over the shape of the airframe (slipstream).
So the take home message for a student is as AC says, don't let the nose come up/slow down too much because you will enter an unrecoverable spin. Obviously as a trainee instructor you have responsibilities way beyond that.