Solution Needed: Scheduled Shutdown Tasks

Perhaps there's a way to do this, but...

I want to do backups and drive defragmentation automatically, and according to a schedule. I could sort of set it up with the Windows Task Scheduler, but the problem with that is that it'll either fire up when I'm in the middle of working, bogging down my machine (and it's best not to have stuff open when backing up or defragging), or it'll fire up when Windows starts, and who wants to wait for backup and defrag to complete before you can do anything on your computer (as if Windows didn't start slowly enough as it is!)?

What I really want is for Windows to recognize Shutdown tasks, much the same way it recognizes Startup tasks. And I want to be able to schedule them. So when Windows recognizes a shutdown task (or tasks) for a given day it completely closes all other applications and non-OS-essential processes, runs the shutdown tasks, and then finishes shutting down when they're done. So when I'm done for the day, I shutdown as usual and walk away from my machine. All that long-running crap happens, and THEN Windows shuts down.

Someone must have solved this problem by now, right? I did find WrapUp, which almost fits the bill, except it doesn't do schedules, and it ain't free (not that I begrudge them that). Thoughts?

UPDATE: Solved!