Check "Fast Boot" in your setting then turn off your phone. It puts the phone in a hibernation state and powers back up in 2 seconds. Should help with your battery 'leaking out'.
Airplane mode is cool, but my whole thing is you have no service in airplane mode..Right? so if you do want to leave on and not get calls, then why not just turn off? If I can get a call in middle of night in Airplane mode then I would switch to that I have never called myself in AP mode, can you get calls?