I used the "invisicord" for my 13 GC. I pulled the moonroof/overhead lighting panel down and used the connector that sits right there in the headliner (its large and white, you can't miss it). It makes for a cleaner install having the connections out of the way. You can then just run the length of wire out of the front of the headliner. The black wire on the far side is your ground and I honestly don't remember which one was power since I've done so many cars, but finding out is easy. Just plug in the ground (-) and then probe the power wire in each socket with the accessory on until you hear the beep of the detector powering on. Then, ensure that the detector goes off when the accessory is turned off (mine in the GC stays on for a few seconds, but turns off with the interior lights). If you're buying an invisicord then you'll need the smaller "blades", they call them "Nissan" size. I made my own "invisicord" out of old phone line by stripping the ends and attaching my own small blades. The radar detector power cord will have four wires in the line, but a standard phone line will only have two. This is all you need as the other two in the factory detector cord are for the LED and the Mute button on the small controller.
As far as mounting goes, yes the larger Escort/Beltronics suction cup mount sucks. I used the small dual cup mount for a long time but recently took off the suction cups and put some 3M tape on the smaller mount. It sticks to the windscreen fine and isn't very noticeable. You should know that mounting your detector high up like that isn't ideal for laser detection. However, I do it since with laser you're pretty much dead in the water anyway. I like having the cleaner install up by the mirror. I ran with that damn power cord draping over my dash for years and I'm tired of it. Be sure that you're removing the detector from the windshield when parking because the sun will fry the components (a good idea for anti-smash and grab anyway).