However, if I turn the entire screen off, by pushing the volume knob in until it clicks, before stopping the engine, then on start-up the radio will be off, but

However, if I turn the entire screen off, by pushing the volume knob in until it clicks, before stopping the engine, then on start-up the radio will be off, but so will the entire screen, which also controls navigation, bluetooth connectivity and the reversing camera. My Subaru has the same behavior, minus the backup camera remaining off. In reverse, the screen turns on and displays the image from the backup camera. It turns off again once you switch into drive. It's certainly a solution to the problem I described, but it's obviously not ideal for all the reasons you've enumerated. Turning off Bluetooth, navigation, and (in my case) Android Auto is certainly a drastic way of dealing with this radio behavior.