What paint on an 8" differential

The doctor is correct on all counts.

But I would not put paint on the axles, why introduce that substance into your oil? You could paint the flanges I guess, but they were bare from the factory and can hardly be seen even from under the car. You could paint the yoke simply to prevent the inevitable surface rust, maybe even a clear-coat too.
 
I did the entire rear end in Por 15 and then top coated it in gloss black. Just like the entire underside of the car. Looks sooo sweet. I even had a classic restorer from down the street stop by while I was working on the body and said that he drives by every day and admires how it looks. (it is sitting up on jack stands to make it easier to work on the rocker panels and lower parts of the body.) You can see the underside from the road pretty clearly. The white KYB's stand out nicely. I like it more every time I open the garage door when I drive up.