I followed the steps on GitHub's website by adding their four IP address records, a CNAME record pointing for my www subdomain with pointing to username.github.io, and a TXT record with custom host and value provided by GitHub.
My domain now says verified by GitHub when I look at my custom domains.
However, when I try to set it as my custom domain for the my GitHub Pages site repo, I get the following error:
The custom domain `example.me` is already taken. If you are the owner of this domain, check out `https://docs.github.com/pages/configuring-a-custom-domain-for-your-github-pages-site/verifying-your-custom-domain-for-github-pages` for information about how to verify and release this domain.