Okay so I finally decided to investigate this problem 23 months later (!)...I downloaded the source (mupen64_src-rerecording-v8.7z) and I think I discovered that the problem occurs when the audio is resampled before it is written to the AVI.
Anyway, I am somewhat embarrassed to report that this problem had already been solved by Bisqwit here:
http://tasvideos.org/forum/viewtopic.php?p=84748#84748. The left and right audio channels are reversed, but other than that the audio sounds great! The audio/video desync problem was apparently also fixed. (I didn't even know about that problem until more recently.)
I would have thought this problem would have been documented more thoroughly. Does this mean that every published N64 TAS on this site was encoded using some obscure copy of Mupen that no one can find, or am I just missing something here?