After more testing I've found out that the name of the zip file is what causes a problem, not the names of the midi files. This is not as bad a situation.
If the name of the zipped file has a space in it, like "movie midis.wzf", and that file is double clicked, the playlist will load with an entry "1. Movie", which is unplayable.
But if the space is removed, like "movie_midis.wzf", and the file is double clicked, the file will unzip in the playlist and the songs start playing.
However, if a zipped file with a space in the title is dragged and dropped into Winamp's playlist, the title of the zip file will display, like "<<movie midis>> (Contains 100 valid files)", does not play immediately, but extracts the songs once the play control is activated.
I suppose much of what I'm describing is expected behavior, though from a user standpoint I'd expect that double clicking an associated zipped file, even with spaces in the title, would work. Perhaps a fix is to adjust the file type association parameters somehow, but I don't know what will work.