New 3D shape plugin!
Changing the origin of the back face should change the object origin. If it doesn't work please file an issue!
Changing the origin did indeed work, I was just thinking about it backwards because of getting too excited.
I looked around a bit and saw that there are already several suggestions submitted for for being able to change the x/y focal point of z-elevation and whatnot. But if it would be a relatively easy thing to implement, adding it now together with simple 3D would be absolutely incredible!