Regarding the recovery procedure applying the full forward stick... IMHO, for many aircraft, that are wing-loaded (most of a/c weight is distributed along the wings--engines, fuel, etc.), this is fine, especially for heavy grossweight and/or aft-CG loading and light twins but for some it might cause problems such as negative G overstress and/or tuck-under (resulting in inverted spin).
I believe that many aircraft (fuselage-loaded) recovery procedures call for stick neutral or just slightly forward of neutral. I read that for some fighter aircraft, stick is supposed to be aft. I guess the bottom line is to look up the proper recovery procedure for the particular airplane.
Ziggy, your question is a tough one. You may not need addtional training if you know what you are doing and it seems you do since you thought the spins were no big deal. My first few spins got my heart beating about 100 beats faster than normal
. Keep in mind, there has been criticism that the spin training required for CFI is not adequate - I heard that it's only one rotation before recovery? If this is true then additionally training, IMHO, is highly desirable. Another point to keep in mind that about 20% of the spin accidents happened with flight instructors onboard.
In a more detailed spin training, right after the incipient spin, you are taught to command ailerons in either direction to recognize the differences between a right and wrong aileron input. You are also taught to observe instruments to determine direction of yaw (which is tough to tell if you are inverted or during night or IMC conditions). Airspeed is very important to tell the difference between a spin and a spiral. Spins recovery inputs are applied after 3 or 6 rotations to show that it usually takes more than the 1.5 rotation recovery the FAA required since you are in a fully developed spin. It also teaches you to be patient and trust your recovery inputs since it would take a second or two (seems like a lifetime) before you can observe the change in the spin. To reverse the correct inputs in a panic would be disastrous. One thing I learned was that the kind of fast and steep spin is the one easier to get out of.