Thanks for posting those links. The animations are very interesting.
In fact tenchi nage (aigamaeate) is most often practiced with the strike to the face in Shodokan dojos, and definitely fits into that second category as the strike's usually done in a 'low impact' kind of a way. (If a 'low impact' strike makes sense - maybe its a blending thing.)
I know exactly what you mean. A few of us played around with variations on what you describe at an open mat session before last night's class. We struck the face, but then went past it to finish the technique.