AutoCAD Inventor :: How To Project Onto A Surface A Divergent Rectangle

I would like to perspective-project a rectangle along its normal onto a spherical surface to create a 3D sketch or curve.

The rectangle is within the volume of the sphere.
The rectangle is much smaller than the sphere.
The rectangle normal may be orientated with any vector.

So for parallel projection this can be achieved by creating a 3D sketch and the Project to Surface command. But I would like to define a divergent angle so the rectangle tapers out towards the spherical surface interior. 

Lofting is difficult or impossible for other factors. the reasons are lengthy to explain here. Is there a surface or solid modelling trick, or add-in, that allows this?