The idea is to actually make a recording. Another friend pointed me to the CMRRA for the songs that have rights associated with them.
Songs that I'm interested in but am uncertain regarding the rights include the following:

Maid in Her Father's Garden
Tom O'Bedlam (in some form)
Cruel Mother
As I Roved Out (the "And who are you, me pretty fair maid" version)
May Morning Dew
Smuggling the Tin
The Flower of France and England
Brisk Young Butcher
John Barleycorn is Dead
Haul Away Joe
Maid on the Shore