These seem like some good ideas, but I'm not a script writer so don't know how hard anything would be to implement - and honestly I have no idea how Jagex identify bots either.
However, some cool ideas would be script degradation. After so many hours, maybe the bot can start missclicking or taking longer breaks between activities or actions to simulate the player getting tired. Or as you said, moving the mouse off screen as if the player is changing song, or selecting something in a new tab.
Right now, a bot can run for 7 hours and do the same thing almost flawlessly. Obviously, not everyone would want this but an option to turn it on/off would be cool. I wouldn't mind my bots having a few missclicks or something hours into a script, as long as it is able to correct itself obviously.