A few other folks have asked about this, and I've been in touch with WP Engine.
Basic idea: pressing save "works" in that it says it's saving, but when the page refreshes, all settings and content is blank.
The popup is created, but nothing I add to it works.
Testing on WP Engine's Staging site works perfectly. That site has no caching.
They ask: "which results and paths are being cached on the frontend?"
I can't find the answer in the plugin files because I'm PHP illiterate.