Why can't I clear the "Composer" field for tracks in my music library on my iPhone?
I don't understand why this is happening to you. My songs are set up the same way (classical has composer info, others do not) and the transfers are fine back and forth with my iPad and iPod when I edit the Composer field.

If you have a Mac, you could try this.

Drag a music file from iTunes to the desktop. Delete the file from iTunes and your iPhone and sync and make sure it's gone. Then drag the music file back to iTunes (with the iPhone powered down) and edit it. Drag it to the desktop, delete from iTunes and put it back, making sure that all the details are as you want them. Then sync to the iPhone.