The device in the sunglass holder isn't the GPS, it is the motion detector for the alarm system. There is a sticker on it to that effect. The sunglass holder is still hinged, it just doesn't have the nice push to release fastener on the front edge. You can open it by very carefully prising it open at both corners on the edge closest to the rear seat. The two screws to remove the overhead unit are inside.
There is a large connector inside that powers the sunroof, interior lights etc. I followed a guide I found somewhere but ended up using a meter to find earth, accessory and ignition for the power magic box. I stripped and soldered to those three wires. I didn't record which ones they were and I don't really want to risk damage to the plastic by trying to open it again to check. There is heaps of room inside there to put the cigarette lighter outlet, excess cable and power magic box.
As you said, I suspect your power run must be somewhere close to the remote receiver or maybe the battery in your remote is getting low? Have you tried a different remote fob or maybe try changing the batteries before you do anything drastic with wiring.