Unfortunately the Smithsonian-Folkways staff is busy moving
to their new facilities, but you could try sending an inquiry.
The Folkways release on their site lists 2 songs not in your list:
We Shall Not Be Moved, and Michael Row the Boat Ashore.
Your list includes 3 not on the Folkways (FTDG, I Need Your Embrace,
and I hope We'll Meet Again) - don't recognize the last two, are they
civil rights movement songs?
Possibly Scholastic simply listed the wrong song titles on the jacket,
unless they are also listed in the booklet - do you have the scholastic
booklet?
You might send an inquiry to the Rodgers & Hammerstein Archive (New York Public Library) which might have a copy of the Scholastic pressing.