Whilst win2k is an NT OS as is XP, I think there are many differences to XP in the interface, etc.
The problem is you may not know if avast is scanning (but the avast icon should be rotating) on shutdown if there is other activity. HJT wouldn't show what is actually running when you shutdown, only what starts on boot, etc.
My best guess is that the disk scan doesn't come from a service being started, but from the shutdown. The avast self-defence will make manual starting somewhat difficult, you would need to disable it, Program Settings, Troubleshooting. You might try something else from that section and that it to Delay loading of avast services after other system services and see if that makes any difference.
Other than that I'm out of ideas, we need someone from the Alwil team with a greater understanding of avast and hopefully win2k.