I won't go into the details here, but the problem "took care of itself." Sure enough, when I was finally able to retrieve my mail, there was this message waiting for me:
Our Mail Servers are working as designed, the error that you are getting is one that is generated by your Outlook or Outlook Express. This is a very common Outlook error and generally means that your "profile" in Outlook has become corrupted. We are sending you instructions on how to create a new profile, if this doesnt correct the issue then you may have to un/reinstall the application itself. Please contact Microsoft if you need help with uninstalling Outlook / Outlook Express as you may need to save your address book / inbox.This was terrible advice, of course. My problem had nothing to do with a corrupt Outlook profile. This left me wondering how a casual email user copes with such nonsense. On the bright side, if it was a serious email problem, at least you would never see this bad advice.