Thanks for your reply, and thank you in advance for your patience as my skill level with WordPress is somewhere between beginner and intermediate.
I deleted both of the Media Library Folders plugins, then navigated to the WordPress update page wp-admin/update-core.php and selected the “Re-install Now” button. Then I installed Media Library Folders again. No change in how Media Library Folders behaves.
However, I can use the standard WordPress “Media” tab to upload an image and place it into a page and publish it. Here’s a dummy page:
http://www.chris-allingham.com/temporary.html
and here’s the image URL:
http://www.chris-allingham.com/wp-content/uploads/2017/06/cooking-grate.jpg
So the folders I thought I deleted using Media Library Folders–the 06 folder, the 2017 folder, the uploads folder–appear to be there in WordPress. Yet when I click “Media Library Folders, I still get the 503 error.