I think I tracked this down to something related to the "Play local file if one that matches Library Server file is found" option. Some background:
The machine on which the 4+ second delay is heard is a client, which loads a library from a server elsewhere on my home net. The media files are on an external disk on the server machine. Sometimes, that external disk is also mounted as an external disk on the client machine. When it is mounted on the client machine, the file names for individual media files are identical on the client and the server.
When the "Play local file if one that matches Library Server file is found" option is true, then when a file is played on the client, it causes the server's media disk to mount locally and plays the file from there. The first time this happens, there is a delay of 6 to 8 seconds. Subsequently - after the server's media disk is already mounted - there is a 3-4 second delay when starting. The difference, 3 to 4 seconds, is the time it takes to mount to remote media disk as a local volume.
The surprising thing is what happens when I turn off "Play local file if one that matches Library Server file is found". In that case, when playing a song, the client still causes the server's media disk to mount locally. This takes 4 or 5 seconds. Subsequent plays occur without delay.
The problem is, with the "Play local file if one that matches Library Server file is found" option disabled, MC is still causing the server's media disk to mount locally the first time I play something, and playback is delayed until the mount happens. I don't think this should be happening. Is there any way to avoid this behavior?