So I gave building one of these a second try and it worked out a bit better. This version is just like the old version, except on steroids and a bit more expensive.
I used another $1 Store Radio as well as managed to fit in some $1 headphones. Instead of using the $1 Store solar lights I instead used three 1.5 volt 50 ma solar cells which are smaller and more powerful. I also used some higher capacity AAA batteries I had.
The total cost of this one is about $6-7. Twice as much as the original one, but still much cheaper than buying a store bought solar radio and far more cute in this Altoids Tin.
Oddly I now have a complete solar Altoids kit setup in my room. Solar Radio, Solar Flashlight, Solar USB Charger... In the event of a massive power outage (or zombie invasion) I think I'm set.