I uninstalled the WP mail SMTP plugin, and followed the instructions here to set up some kind of mailserver or something:
http://blog.techwheels.net/send-email-from-localhost-wamp-server-using-sendmail/
...and to my utter shock and surprise, it actually worked! Well, all emails (regardless of who sent them) are 'from' me, 'to' me. But heyho, it's Windoze, you can't expect it to work properly.
- Paul