Hi Ryan,
There is an issue with the "Insert link" function when the link contains a Font Awesome HTML tag : when you edit a link, the text is duplicated inside the <i> tag.
E.G. If you edit this kind of HTML structure
<p><a href="https://www.joomlacontenteditor.net/test.html"><i class="fas fa-address-book"></i> This is a link</a></p>
After edit the code becomes :
<p><a href="https://www.joomlacontenteditor.net/test.html"><i class="fas fa-address-book"> This is a link</i> This is a link</a></p>
You don't even need to make any changes, just click on the link, click on "Insert link" and then click on "Update"
I've tested with JCE 2.9.18 and on your demo website.
Best regards