I was happy to find this little plugin. It seemed to be exactly what I need: it claims to take text from the header image’s description field and print it out with a short bit of PHP.

According to the readme, if no text is in said field, it is supposed to print out the site title and description. Unfortunately I find that it only prints the site title and description. It ignores text in the header image description field.

https://www.ads-software.com/extend/plugins/header-image-description/