Here are a couple of things you may like to chase up:
1. There was a CD devoted to old recordings related to the disaster, not the crap on the film. I had a track listing of it, but seem to have lost it. The details are:
Titanic Songs Original Phonograph Recordings Honoring the Disaster, Recorded 1912 to 1948 Various Artists Unsinkable Music TSCD-22798, 1998.
I have a note that 'Usinkable Music' is Joe Showler of Toronto. Perhaps a Canadian 'catter can assist in this regard.
The CD was reviewed in 'Old Time Herald' Vol 7, Issue 1/Fall 1999.
2. The New York Public Library evidently has a list, compiled by a Solomon Goodman, of songs and musical works related to the Titanic.