Re: Aikido techniques are structured around six main pillars?
They come from Rinjiro Shirata. I do not know if Shirata Sensei used the word "pillar" or not but his book, written with John Stevens and entitled Aikido The Way of Harmony, follows this basic scheme.
It has been interesting for me to learn that the history of Aikido teaching begins with the various students of the Founder attempting to structure what they learned. Morihei Ueshiba taught rather freely it seems and the students found they could not duplicate this when they themselves became teachers. I believe that is why we have some many "styles" of aikido now, even though them all stem from the same source.
Prof. Stevens' comment on this is that we are not likely geniuses like Shirata Sensei was, so for us, Shirata Sensei created certain forms.
a side note - kotegaeshi is considered a kaiten technique