I just had another thought on the extending the power supply cable.
One of the four wires in it is the common. Maybe you are extending the boards ground plane.
If you decide to move the antenna wire external.
The bottom cover does not come off when the five screws are removed.
There are a few catches holding it on. That is how I damaged my case. Popping the catches.
All the electronics are mounted on the top cabinet piece except the siren sounder. Its assembly is clipped to the bottom cabinet piece with a pair of wires to the main board.
When you put it back together. Make sure the positive battery terminal soldered to the board. Goes back into the slot in the battery holder on the bottom. Guess you know how I found that one.