So I downloaded a db snap from 8.3 and then re-applied the 8.4 update and took another database snapshot. Then I diff'd the database snapshots. The biggest changes seemed to be in the cache tables and removing and adding some revision columns. So I reverse-engineered a backgrade SQL script. With that, I updated the composer.json file from this:
Now I just need to ignore Drupal telling me about 8.4 until I'm ready to fully embrace PHP 7. I feel like something bigger needed to get my attention to the update in system requirements when I ran the initial composer update.