I don't exactly have an answer for you, but I have a source you might try to find. The ILGWU began publishing its own song book in 1935, and by 1973 had published at least a half dozen editions. The 1931 edition, called "Everybody Sings" has 30 garment workers songs.Another possible resource is the conference on labor songs held every year in late June in DC. I have a friend who goes to this, if you'd like more info.
Perhaps Joe Hickerson, or another librarian at the Library of Congress could help.
Good luck. You're right-it is a great topic for a song.
Mary McCaffrey