Thanks to some external help, the issue was identified to be that my redis cache hadn't been flushed prior to attempting the upgrade. Since I had done this upgrade and tested it before on the staging server before attempting to promote it to prod, the redis cache already had objects from 4.7.6 in it, despite the database reflecting the actual, older version.
Although this didn't happen to me on the dry run, I did have other errors because the new server originally didn't have redis on it when I first started testing this upgrade, while the old server did. Lesson learned: always disable caching prior to upgrades.
I kinda wish that was in big bold letters in the upgrade manual, though...
