Take this doubled over piece of tape and forcefully shove it toward the back of the flash camera unit. This will trigger the pop-up flash latch release inside the camera and allow you to continue the disassembly without ever needing power!

Those two little screws are the culprit! The funny thing is the previous camera, the Lumix GH2, also featured screws here, but the pop-up flash had a manual switch! I guess the designers forgot about this when they implemented an electronic flash trigger switch.