CRM/Core/Config.php line 41 throwing 500 error with new require_once api/api.php
First, let the record show that I am an idiot.

After uploading 4.7.23 (the new version) to /wp-content/plugins, I neglected to copy the pre-existing civicrm.config.php into /wp-content/plugins/civicrm4.7.23/civicrm ... thereby depriving the system of (at very least) a working value for $civicrm_root.

It was suggested to me that my civicrm.config.php was probably off, and I checked it just to make sure the $civicrm_root value made sense. The value was good, but the file I was checking was located outside of the plugins directory -- this was a clue, and I missed it. As I said, I'm an idiot.

Of course, once I copied the old civicrm.config.php into the new /wp-content/plugins/civicrm/civicrm, everything worked perfectly. Except for CRON jobs, of course -- but that's another matter.