Thanks. It appears you solved the problem.
I’d reverted to stock themes, disabled every plugin, spun up a new database and Wordpress instance, etc. Nothing seemed to fix it, and I could load Wordpress and the same content on another domain with no problems at all.
In a nutshell, if I clicked on each of the pages on my web site, at least one or two wouldn’t load and I was starting to get failures from Google Webmaster Tools, which would eventually cause my SEO performance to suffer.
It certainly appears as though you fixed it – I’ve tried several browsers on several machines. Thanks so much for your help!