This photo shows the case itself (the pink thing in the back is a stick-on LCD flashlight) and the charger. The charger is clearly too wide to fit through the bottom, making it impossible to charge the iPhone in the case.
Step 1: Tools, and safety first
Be sure to wear safety glasses and a mask any time you are sanding if you value your ability to see and breathe. Seriously. Plastic dust is pretty toxic.
Oh, and I had my iPhone playing music in the background while doing this - awesome!