I have a tire mix like yours Mike, wider for the back. Same issue, fronts are fine, rear are brown. It's a p*ss off! Can't find anything that says the issue has been corrected by Goodrich.
Here's an easy fix for those with the Goodrich TA's. I think I must have gotten a mix of old and new stock. My front tires are fine but the rears are browning. The new runs are problematic.
I bought mine, Goodrich radial TA's, a few years ago. My fronts are fine, but the rears (wider profile) are turning brown. Any attempt to clean or make them look better is temporary.
Not sure about the Goodyears, sorry.