Phantom Email Window Keeps Appearing in Apple Mail
This seems to be caused by incorrect credentials for the SMTP server that had been associated with the from address of the email. The Inbox for that email now has " - dead" appended to it's name (presumably referring to the SMTP server not working, as am receiving emails). It's a gmail.

As a workaround, first, I can stop the annoying window's phantom behaviour by taking all accounts offline ("Mailbox" menu). Then change the SMTP server for the offending account (fix credentials or use one that works), then re-enabling all accounts. At this point, the phantom email is actually sent and everything seems back to normal.