3d scan of imperfect globe to a 2d Equirectangular Projection

[Vigilus]

there normally will be two ways to do this

for cycles and nodes ( better results )

move blender into cycles render
check " use nodes" box in miterales to creat a new node set up
After this text is where I'm having the issue------add a new image texture node and in the drop down menu should be the textues name you are using for the oddly mapped textuer

add a emission shader ( this will cause the texture to glow)

add a camera at the center and set it to equal area projection
( you might need to rotate X + 90 degrees )
--- sounds very complex but really it is not
and render

Normally, just to see my texture at all I have to be in texture paint mode on the object while the object is selected in the scene.
When I go to materials I don't have any drop down menu showing a selectable .jpg texture file.
The texture on the added material is all white, even when I rename it to the existing texture and select the new one.

Thanks for taking the time to give an more detailed answer!

add a camera at the center and set it to equal area projection

---Do you mean Orthographic Projection?