Thanks for your input, Graham.
The "versions" people do doesn't matter. All the versions, if executed correctly, correspond exactly to the movements of strikes.
Let's take kote gaeshi as an example. kote gaeshi, means 小手返, "forearm return." The technique "kote gaeshi" doesn't work from any turning of the wrist. If people think that, they don't really understand the principle behind the technique. In fact, I think the name "forearm return" gives a much better idea of what's really going on. The forearm of uke is returned back into their center - in a spiraling motion. The force is applied by nage on the X axis through uke's center.
The following video has very good examples of tsuki wasa. And you'll notice that the movements of tsuki are exactly the same movements in gote kaeshi - regardless of the "version." Every kote gaeshi begins with nage's outside hand moving - capturing uke - and then turning palm-side down. Then as the outside hand begins to rotate back into a palm-side up position, the inside hand comes in and rotates to a palm-side down position. And kote gaeshi is executed. Nage's hands, hips, and body move in exactly
the same way as tsuki.
If anyone reading this does a few of those tsuki combinations; left-right, and then right-left, and then looks at what they do with their hand movements in kote gaeshi, I guarantee, they'll think, "Damn, that guy is right. That's exactly what I do."
Kote gaeshi is
I can see the concept you give and that's fine. I can see that done that way it has the same movements and 'thrust' as tsuki. So that's fine. So the way you put it above comes across better to me than mentioning axis. So that's all good for me anyway.
However, your description of what kote gaeshi is - is one version. As I said there are more versions than just that one and there are versions which don't then fit the analogy.
That said, if your purpose is to show the relationship of said version to strikes then fine. If it's then to show the relation to sword then I take it you are saying that's also the same as a sword thrust. O.k.