Return of mail!
Chaos has solved my problem; she pointed out that Pair lets users use port 2525. So I changed my email settings to use that port, and everything now works.
Thank you, Chaos! Extremely much appreciated; that'll make the next couple days a lot simpler and less frustrating, not to mention any future times when I run into the same issue.
Thanks to others for suggestions as well.
Tom's suggestion of using gmail, and my reaction to it, underscores something I hadn't quite explicitly thought about: the preferred model for email these days seems to be to keep mail on a centralized server and access it remotely, whether via a webmail system or by logging into a UNIX shell or by using IMAP. And that model just doesn't appeal to me. I want to have all my mail on my local machine; I want to be able to search it quickly, and to have it with me when I'm offline. (Which is kinda funny given that about 90% of the time I have broadband access in one form or another.) If you have mail on a server, you can access it from anyone's computer, which is cool; but if you have it locally, you can read and respond to it and sort through it on the plane (even though you can't actually send or receive it), which somehow is more important to me. Odd.
Anyway. The return of my ability to send mail underscores the fact that I haven't actually written responses to various recent messages, so I should probably do that instead of journaling.