I don't know the answer to Alan's question (What is the name of the Russian folk song used?)

However, I have found a MIDI of the Round Dance of the Princesses

http://www.kunstderfuge.com/stravinsky.htm

When I saw the Firebird performed, it occurred to me that The Round Dance of the Princesses could be a nice number for my band, which has flutes,recorders, harp, and guitar. I had no idea how to find a MIDI. Now I have it.

Now to use music software to make the piece accessible to my friends...