I’ve discovered something interesting, if I’m right about it. The storage externally accessible in MSC mode seems to be disjoint from the storage accessible in MTP mode. In other words, the files you place in the MUSIC directory in MSC mode are invisible in MTP mode over the external cable and vice versa. The files visible in the device are the set union of the files in the two modes. There’s a Playlists directory visible in MTP mode but not in MSC mode. (I don’t know about directories such as Podcasts.)
Is this really what’s going on?