Its not a brilliant height map, but here it is.
Not a full solution for YOUR problem, but it's one way of solving it: Unwrap the object to the shape of your map. Most 3D-modelers have this tool (3DSMax is reasonably simple). It flattens the mesh over an existing bitmap.
This flattening of the mesh will not place itself automatically right over the map, but you can edit the flattened sphere mesh to match the shape of this projection in the unwrap editor.
I don't know exactly how to do this at this time and, and might not get around to make an example to show you within a reasonable time. So just take this as pointing a finger in a direction. Maybe someone else can come up with the example before I can.