I don't quite get how you're using the terms x, y, z axis
. I understand quite well what the x, y and z axis are, but in coordinate geometry (which is, after all, where these axes are defined), the x, y and z axis never move, and in your model, they appear to do so, sometimes with reference to one partner's body and sometimes with reference to the other partner's body and sometimes I'm not sure what.
It is possible to define a coordinate system that moves with respect to some other frame of reference, as long as it's self consistent within itself (i.e., x, y, and z can move with respect to the earth or with respect to the solar system, etc, as long as they keep their relationship to each other). Not sure if that's really what's happening here, though.
yonkyo = shomenuchi = cutting on Z axis
If you're doing shomenuchi in such a way that you are only moving with respect to uke's z axis, and not their x axis, then you're doing something I've never seen before.
I think what you're saying makes much more sense if I mentally delete all the x, y, z stuff (which seems to me either inaccurate or unclear) and just leave the observations that some techniques use similar movements as some strikes.