Can I add another aspect to consider when defining an 'incipient spin'.
Let's first consider what defines a 'fully developed' spin. This is one in which the mean axis about which the aircraft is rotating is vertical. The aircraft will have pitch, roll and yaw rates but there will be an earth referenced axis about which the overall rotation occurs. Any consideration of the balance of inertial and aerodynamic moments relates to whether the spin is oscillatory or non-oscillatory. For example, if the moments are not balanced but the rotational axis is vertical then the aircraft will be in an oscillatory, fully developed spin.
Immediately before the control inputs that cause an aircraft to spin are made, it will have a flight path which inevitably is not vertically down as will be the case in a fully developed spin (you can flick-roll on a down vertical but airspeed will generally be too high to enter a spin). Therefore, there is another phase of the manoeuvre between entry and the fully developed spin, and this is what is generally considered in my world to be the incipient spin. This may last anywhere between about 1.5 and 4 turns from a level entry but could well be as high as 6 turns from a manoeuvre. It very type specific and also varies according to the aircraft's flightpath and power setting at entry.
In my opinion, what you do with the power in the recovery from an incipient spin needs to be type specific because the effects of propwash, torque and gyroscopic moments vary from type to type, and direction of spin along with being erect or inverted may require different optimal power settings. And let's not forget that jets spin also! However, for training simplicity and safety it is best if the recovery from the initial stage of an inadvertent spin is the same as that from an unusual attitude recovery and therefore some degree of compromise may be necessary to achieve this so long as recovery from a spin is not prejudiced.
I fly and spin one type that when centralising the controls during an incipient spin, as defined above, often does not result in recovery. This is the Harvard in a right, idle power spin. Any more than 1/2 turn and it requires at least 1/2opposite rudder as well as neutral or forward elevator to recover. I accept that we do not attempt this recovery power on, in deference to the age of the aircraft, and so I cannot say whether or not that would improve recovery characteristics.