This is a Windows 2003 (or later) machine that gets switched on every morning, but no one logs on until some hours later.
I want to use the time in between to run a back
The way you aleady do this seems fine to me; however if you want an alternative approach then services get started when the machine boots so you could write a service that detects if it's a new day (to allow for reboots) and if it is then run your backup.
If I was doing this as a service I'd use TCL because I know it and like it and it has an extension twapi that allows you to run a script as a service. Other scripting languages may well have similar facilities.