You should go through PRS. Whether the writers are alive or dead, or "relatively obscure", there is copyright involved and unless they've been dead long enough for the copyright to have elapsed someone is entitled to receive the royalties. You don't have to track down the labels. The song is the important thing, not the recording of the song. Labels own the recordings. The copyright of the song will have been left to an heir.

As to whether or not the writers "very much intended for their songs to be part of a folk tradition" - the holder of the copyright will be aware of this and may give their permission for you to record without payment, but you can't take it for granted and simply bypass the system.