Okay, I tracked it down (maybe). I was reviewing the HTML output, and at the bottom, I found Cloudflare javascript with caching active, which it shouldn't have been, as I have cache bypass rules set. I created more precise bypass rules and then enabled developer mode. That did the trick, even when taking it out of dev mode.
However, here's the thing: I've always used Cloudflare and rarely interact with it. I've never had a problem with anything else on the site. And I've never had a problem with MB and Cloudflare until (it seems) the last update.
