I finally had the time to dive back into this, wondering if I was going to just have to rip it out and start from scratch, BUT THAT WORKED! Thanks so much, @gretchenlouise!
I’ll give emailing them a shot.
Unfortunately, the problem persists even with all the plugins but MyBookTable and Essential Grid turned off, and it continues even in other themes.
I had a similar problem yesterday. My blog at Forbeck.com/blog spat out five posts to my social media accounts from 2005, 2007, and 2008, seemingly at random. I checked on the Sharing settings page but couldn’t see much to change. Then it stopped all by itself.
I believe these were all posted natively.
I noticed that my LinkedIn connection had failed again, despite me reconnecting it after it failed earlier in the week. I don’t know if that has anything to do with it.