My new iPhone 4 lens arrived this week and replacing it has resolved my foggy photos! I have brought out my old case again as well, so I hope to not have to replace the lens again for the rest of the phone’s life. It is strange to say, but the only issue I encountered was getting one of the two bottom-side screws to thread back in properly. (One is still not in the entire way.)
Here are photos of my new tweed Fender Pro Junior before and after replacing the lens, taken in the same room. The photo taken with the new lens (and no cat) has a much better quality.