As it turns out, those things wedge themselves into places pretty good. With a nod to all professional IT techs, there are a LOT of little spaces for viruses and their applications to hide.
A lot of the bulletin boards tell of people who dealt with the problem for eight hours with no result, some who are still dealing with the problem days later, and other who said "Screw this, I'm going to the Apple Store." Me, I was determined to kill this thing dead. So after failing to solve the problem with my limited search-and-destroy skills, I hunted down the proper removal tool, ran it in Safe Mode, cleaned the registry, and reset Internet Explorer 7. At that point I had everything but the homepage hijack taken care of, so I reinstalled Internet Explorer 7, reconfigured that, and tried again.
Success.
I didn't get in to work until about 10am, though. They think I was dealing with a "mild utility problem" at home. If they ask, play along--but the merit badge is MINE.
