If my time counter is the same as yours (though I use Windows Media Player to watch DVDs), there's a music track that starts when Phlox starts reading his letter from his doctor friend. David Bell is credited as the composer for the episode, and Steven M. Rowe is the music editor. However, I'm deaf in one ear so can't accurately listen for any possible reference to a traditional tune.
BUT, there is an acknowledgement to the film For Whom the Bell Tolls
, which was the movie night feature I believe. It's possible Bell was doing a variation on its film score.
You might be able to track down Bell or Rowe on the internet somewhere and ask them specifically.
I was impressed by Bell's score for VOY: Dark Frontier, where I first became aware of his name.