I've thought about the idea for a fair amount of time after getting shut down last time. Why not separate the audio from the videos, align them correctly, and then align the videos (and mute them) with their matching audio?
I tried it, and voilà, it worked!
I hadn't had the time to figure out how to do it, but since I'm on break, and after downloading AoA Audio Extractor, it worked like a charm!
My next post will be the fruit of my labors.