When I moved the router I just ran an extension cord from the back where the inverter is up to the bedroom dresser where the router rides. I carry the extension cord anyway, so it was the easiest route to go.
I have had real good luck with the app, note I am using the free one and there is a paid one, but never used it. We have it on 3 apple devices, and 4 android devices and have not had any issues out of it. We use the camera's at our house so they get a good workout. I personally prefer the app on the ipad as it looks a little different, and I think is a little easier to use.
I really liked your idea for the rear view camera setup, it sure beats the price of a Voyager system for $700 that I have been researching. I followed your links, and the the router has an updated model, I think I will get. I have a Nexus tablet and the first Ipad I can use the truck. When you moved the router into the bedroom, did you need another inverter? Also, does the app work well for you? I looked at the Google apps store and the android app got so-so reviews. If the apple app works better I will use the Ipad.