I have the same cab and chassis under a 2014 Itasca. My radio is a Pioneer unit, with a back up camera wired into it, with the same how do you shut it off issue. I found that in my case if you open the door it will shut off the radio (and the back up camera) when the key is removed from the ignition. You can also shut it off by using the touch screen and pushing the off icon for the radio, although sometimes other functions start up when you do that. Mine is wired into the cab ignition and not the house battery. My Coachmen with a regular stereo is wired into the house battery.
My biggest gripe with the Pioneer radio is there doesn't seem to be any scan feature - there's seek, but no scan.