I was right; recording audio and video at the same time is way, way better! At least for me.
I gave the other voice-over episodes a re-listen, and they were awful— so much disconnect, so robotic, not natural at all.
For the final episode of the series, I recorded the audio and video simultaneously, and I loved it! I still had to do lots of takes, cut lots of umms and ahhs, and awkward pauses, but all in all, it was better than all the other lessons I voice-over on.