Ok, not something I can fix with a simple setting change in Events Manager then.
Yes indeed, that was it. I found the media prefix setting under setting > media and made all images use https. Everything’s displaying normally, now. Thank you for your help MarkRH.
FYI, anyone else banging their head against the same wall, I solved this problem by uploading images specifically sized to occupy the space I needed to fill on the page.
I think there’s a bug in there somewhere, but I don’t have the know how to figure out where to look for it.