So I found that my auto-linking to Facebook (visit me here) was having difficulties with the various thumbnails I had been posting. Apparently there is a restriction on Facebook that images need to be larger than 200×200 pixels, and my thumbnails were sized at 150×150. As a result, each post would get an error on the picture, and then Facebook would randomly select the next qualifying image from the page. As a result, it would either post my Patreon icon, or other irrelevant images.
I have now corrected that issue, and although the thumbnails on the site will be a bit larger (225×225), this should allow future Facebook posts to come across cleanly without the inherent confusion.
Gotta love all this complex technology 🙂