Wow, I am trully fascinated how many messages went into a simple projecting issue.

You know as a 3D artist I have to deal with this all the time, scanned objects have bad topology and their UVs are all over the place.
I know this might be a bit late but to me the problem is simple:

-You have one object where the texture looks nice when wrapped but the UVs are a mess.
-You can make an object that is exactly the same but with a better UV layout. For example in Blender you can create an UVSphere and select automatic UVs, you will get an equirectangular projection.
-Should you also want to transfer to the new sphere also geometrical deformations I would go over to zbrush to project the geometry to the new perfect sphere, but I believe there is a way of doing it in blender using one of the modifiers that changes the shape of one object to a target, thus you would en up with two identical spheres but one having correct UVS.
-If the objects match up, with a program like xNormal you can project the texture of the first object to the new sphere, and voila.

I hope this helps a little bit at least, maybe I am not getting the real problem,

Daniel.