Fixed. It turned out that my public key was wrong. I found it with...
https://dkimvalidator.com
This website gives you a random-ish email address. You go to your mailer and send an email to this address. Then click, and it gives you a voluminous report about the DKIM and SPF characteristics of the email and your
domain.
I copied the public key into a file on my server. Then copied the "key" part of the key file into another file. Then compared the files, first with diff, then by loading them both into a text editor and bouncing back & forth between them. Strangely, the first several characters were the same, and the last several characters also the same. But characters in the middle were different.
I updated the public key in my DNS and all was well.