Correction -I may have the same system. I recognized the Garmin BC-30 camera but I don't know what you have on the receiving end.
I've got the Garmin Drive Assist 51 LMT-S as the GPS/dash-cam/bu-camera receiver. Most of the time it works pretty good, even better with the software update. It does not run as hot any more. On occasion it says a cable is disconnected and on occasion it does not link up with the back up camera.
I don't use the Garmin Smartphone link. It can't be turned off on the android phone once installed. That is the one thing I would like them to change. Installing and uninstalling is a PITA.
In my TV, a 1st generation Ridgeline, I picked up an aftermarket tailgate handle that has a space and opening for backup camera. That was an option on later model years. It took a little MacGuyvering to get the BC-30 to fit. I put the transmitter on the drivers side behind the
tail lights.
I'm glad to hear yours works over that distance. Are you able to use Voice Commands to show/hide the camera view while driving on your setup? Voice Commands are cool once you learn the syntax.