I've setup a file which demonstrates the principal of how to convert painted "paint sop" colors to a texture map. I've rendered two images. One is the flat 2D texture which my client needed. The other has the original sphere with the colors painted on using the Paint SOP.

Basically, I use the uv coordinates to pull the color information from the sphere over to the grid. Then render the grid as a flat surface which can be a image map texture for rendering.

The ortho cam render is the final baked out map. The perspective render is the proof-of-concept render.


Here's some hints.
1) You'll need to think about which projection type for the sphere and the flat objects (not the same.)

2) The sphere is not one from the sphere SOP but I used three other SOPs to make it.

3) The flat plane is not a grid and I used three SOPs to make it.

4) Use vertex textures, not point textures.

5) The key expression function to get this to work starts with the letter "p".

Good luck!

Let me know what you come up with.