Im assuming that's a 9v battery compartment? Could those battery tabs be connected to the PCB and just pushed through/clipped into the outer housing? Maybe those battery connector tabs could be pushed through the back?
When you mess with the cover, where does it feel like there is resistance?
You could try to use your phone to take pictures between the cover and the guitar body, it seems you can move the cover some, but idk if it's enough.
Systemd is great fuck the haters