In a backchannel conversation, I was asked about what is involved in setting up webmentions. I responded there, but thought that I would keep a note of it here:

Hmmm, my suspicions to why my webmentions/linkbacks are not getting through is that they are being flagged as spam by spam filters. On the WordPress Webmention Plugin page, there is some code that you can add to functions.php file to prevent this:
function unspam_webmentions($approved, $commentdata) {
return $commentdata['comment_type'] == 'webmention' ? 1 : $approved;
}

add_filter('pre_comment_approved', 'unspam_webmentions', '99', 2);

There is also More on Webmentions on the IndieWeb.org, but really it is a part of the IndieWeb plugin.
I was never really interested in endless mentions under my posts until facepiles.
In the end, it is a very technical solution at this point in time, but I feel it is worth persevering with. Like Chris Aldrich, I am not sold on Mastodon as the supposed solution to the social media and the web, but feel that there needs to be something better than FB and their shadow profiles.
Here is to hoping.