telinit 1 and run a command there

I need to do some maintenance on a bunch of Debian (Wheezy) systems, and it has to happen at run level 1. But not all machines have a keyboard and a screen; some are even located somewhere else. So I can't just go there and type in the root password to trigger the job. So my question is how can I tell Debian to run a command right before the "Type root password or ^D" prompt? I've tried to make a init script that only runs on run level 1, but still it was triggered before all processes where killed. Is there a way to do this?