Time Machine did not finish backing up because some files were unavailable. Backups will resume when your Mac is unlocked.

After my initial post, I tried erasing my backup drive and starting over with a new time machine backup, but I still got the same message.

After exhausting everything I could think of, I called Apple Care. I spoke with a representative who let me explain everything I had already tried and he indicated that I had covered most of his solutions matrix, so we didn't waste time going over that again (GREATLY APPRECIATED!). I was put on hold for a short time by the rep then asked to do the following:

1. Eject my backup drive and disconnect it from my Mac;
2. Open time machine and tell it to forget my backup drive;
3. Restart my Mac in Safe mode;
4. Reconnect my backup drive;
5. Open time machine and tell it to use my backup drive for a new backup;
6. Let time machine format the backup drive and complete an initial backup to my backup drive;
7. Confirm the initial backup finished without errors;
8. Restart my Mac in normal (not safe) mode.

I completed the above steps in pretty short order and have since had 5 hourly backups with no errors. This seems to have solved the problem.