Don't know if this is helpful, but...
Of course music cataloging needs differ and might not match standard MC. To the rescue rides the wonderful MC capability of custom fields, so you could have separate tags for Words and Music. But I just want to mention what a quagmire that might be.
I use MC's standard Composers field, entering the one or multiple people who are credited with the song, all in one field, delimited by semicolon.
I don't try to identify who wrote words and who wrote music, because so many songs either lack this degree of information, or they were collaborations with no identified separation of roles. For the songs where roles are known, to be precise would require multiple fields...just for those songs. It would be quite a challenge (and mess) to have composer info scattered among separate fields. I could find all the melodies composed by Larry Hart by looking in the Words field, but where would I find all the melodies composed by Freddie Hart, who wrote both parts of his songs (then performed them)?
Many songs in my library are cross-over efforts, two or more contributing to words and music -- sometimes including the performers, modifying the song in the studio. The Beatles music, for instance, ia all credited to Lennon & McCartney though they had various degrees of involvement, including songs known to have been composed by only one of them. Then there are the songs where the rest of the band and notably George Martin made key contributions, not credited anywhere but in books and album notes. For tracks where such detail matters to me, i put song (and recording) background info in a separate text field; MC has at least two, Comment and Notes, though custom fields could be used.
Even composing of the "standards" is messy. Some is well-known and cleanly defined, but many have mixed parentage. While Rodgers and Hart, Gershwin & Gershwin, and similar have known roles, many other songs of the same era just list multiple names, implying a true collaboration.
So, I put all the names in Composers. I rely on my separate knowledge of how Rodgers and Hammerstein divided up the work.
But when details about the song and/or recording might not be so obvious or easy to remember, I use MC's Notes field, which can hold a large amount of text.