How are you using the remote turn on signal with the amp? Are you using a JL amp with auto signal sense? If so make sure it is activated if you are using the high level inputs. I had this problem with my challenger until I switched to high level and activated auto signal sense.
On the flip side. I have a 2013 BOSS and am looking to make mine sound a little better as well. I am wanting to install all of the shaker system. I have new door panel with the 8" mounting but am having trouble locating the part number of the factory amp and if the wiring is already in the car. Some pictures of the factory amp would be great. In a few more days I will have a 2013 Ford service manual DVD in my hands if you need any wiring info.