I just saw yesterday that FTP7 was out. So of course I went off to install it. When I was done, the Default Web Site on the server no longer worked, including Outlook Web Access. Much panic ensued, as in the past OWA has been very finicky and once broken it stays broken.
It turns out that I had uninstalled the IIS6 components as part of cleaning up before doing FTP7 (I had installed the IIS 6 things for FTP6). I'm not sure if IIS6 components and FTP7 can live alongside each other as I uninstalled FTP7 when trying to get the site working, but I would guess so. Anyways, simply re-installing all of the IIS6 components fixed the problem.