I have a feeling that what I am about to say will not be quite what you wanted to hear, but for what it's worth...
I too use MM with a lot of classical music, and I think it is the only player/organiser which allows a reasonable organisation of Classical stuff. I had an issue with the layout I wanted and felt I needed to introduce the concept of the 'work', which is, I think, the same as your 'composition'. The only way I have been able to introduce it to MM is to use the 'Album' as the 'work'. If a CD has two works on it, say Beethoven Piano Concertos 1 & 2, the CD must be ripped twice (I usually use dBpoweramp's CD-Ripper, but it should be the same for MM I guess) so that you get two 'albums', one for each of the concertos. In addition, much of my digital music is digitised from LP using a CD recorder in my Hi-Fi, and it is straightforward when tagging the newly recorded files to name the album as the work, and this should be true for music you have already ripped (I would think). In addition to this, and equally important, I ditched the rather silly catch-all 'classical' genre, and always substitute my own when ripping or editing the audio files; these are the usual genres in common use, for example: Concertos, Symphonies, Chamber etc. You would of course set these to suit yourself, but once chosen the categories must be adhered to rigidly. It all seems very complex, but once you get used to it there is no problem really.
I thus end up with a listing, of the following form:
Composer => Genre => Work & Artist/s* => Track number & Title. * Note, I use the [i]Album and Album Artist[/i] combination from MM because it then sorts and groups the files properly.
This is matched by the folder/file layout on disk, which is:
Composer => Genre => Work => Artist/s => Track # and title file (i.e. the actual audio file).
I hope this is of interest and I apologise if it is not...