Been following this thread for quite a while, so I guess I might as well contribute something...
I have a #3 cam that wouldn't turn on after charging it for several hours. I was monitoring the USB current while charging, waiting for it to drop, but it was just sitting at 120 ma (after starting out a little higher). Opened the cam, measured the battery voltage...0.0V...nice.
I went ahead and bought a few cheapo 240 mah lipos off ebay because the dimensions seemed close enough and this is what it looks like now:
The first charge was good for 67 minutes, but unfortunately the 240 mah batteries are really too thick for this cam at 5.5 mm. It's possible to close the case, but it takes so much force that it looks like it's about to pop open, and I actually had to shave like half a millimeter off the plastic buttons because the circuit board was pushing down on them and triggering both. It sorta works, but it's a really dodgy solution, and putting it together requires a magnifying glass and very steady hands, because there's not a fraction of a millimeter to spare anywhere.
If you're thinking about replacing the battery in your cam, I would not recommend using the 240 mah lipo packs on ebay. The JST connectors fit reasonably well though.
I'll be testing this contraption soon, but I'll probably have to use some duct tape to make sure it doesn't bust open and spill its guts in flight.