Alright, folks, I've got good news and bad news.
The good news is that I am on a fresh install of XP SP3, with Avast running just fine.
The bad news? I don't know what happened those two times previously to cause such an irreparable login loop. Oh well. My advice to anyone is to fully update your Windows XP install before installing Avast, just as a precaution.
As an aside, this was probably the longest install of XP I've ever done. XP, for whatever reason, didn't want to set itself up on a C: drive, but instead an H: or I: drive - I don't know about the rest of you, but it drives me nuts if XP isn't on C:. So I spent a couple hours going through the registry and changing every reference of I:\* (mostly using a 3rd party registry editor with Find & Replace capabilities, but some I had to do by hand). After making the changes, I did a cold shutdown of the computer, and booted it up - and voila, C:\Windows.
Anyone who ever told you that you can't change your boot drive's letter after install was wrong
But it is, however, a pain in the butt.