Found the solution – it was actually the Advanced Custom Fields plugin that was blocking it. At the very bottom of the ‘edit field group’ screen (for ACF), there’s a big box called ‘Options.’ I had checked Featured Image as being a metabox I wanted to hide. Once I unchecked it and saved, I was able to go into the screen options on the Add New Exhibition screen and tell it to show, and there it was! Apparently I had played with the ACF configuration since moving the site from localhost to the server.