I really have to emphasize that the field outside the sphere has an x and y component, so that this answer is incomplete unless I am interpreting it wrong. If anyone is interested I can post my own answer and take the time to LateX it.
The statement you made that outside the sphere the field is a superposition of a homogeneous field and an induced dipole is right but I believe you are omitting the x and y components. I do not quite see why you drop them.
