I couldn't help myself - it was at least worth a shot. I tried taking apart two speaker types (magnetic and piezo), and fitting them into the pocket at the bottom.

Neither one worked - the piezo was too small (not much left of it) and too poorly supported to allow much sound to transfer at all.

The tiny coil I wound was much more like a short circuit than a coil (don't worry, there was a 220 ohm resistor in there) and got no sound output at all. But I feel that with many more turns and much finer wire (like the magnetic speaker had originally), this one stands the best chance of working.

I feel like there is a cell phone / ear bud / hearing aid speaker made for a size this small, but I can't put my finger on it.

This youtube short (yeah, sorry) sums up this evening's events.