I just use the stop.php in the tmux directory.. takes 5 minutes, but it seems to actually shut down all my scripts in less than a minute.. Then i do a tmux kill-session -t nZEDb .. nZEDb is what my tmux session is named.. I can't remember if that is default or not.
I use the start.php to start my tmux... you can make an init script.. there are plenty of examples on the internet for Ubuntu.. You just need to make sure it starts up after apache, mysql, etc start up.. You can set a priority for all your init scripts..
How are you doing your system backup? rsync?