How do I make backfaces override transparency into a flat color? I want to be able to change the outer edge seen as A into B where the transparent part is shown as green.

As long as it looks like the B version on this image.
Without changing any aspect of the inner sphere. 
While keeping the toon shading as is.
Without adding any additional mesh.
You can use nodes to set different materials to the front and the back faces.

In your case, I would use the outer mesh exclusively for the outline, with a node material:



The green materials is shadeless.

Then, again using nodes, you can mix the shadeless and the toon shaded materials for the inner shape: