Hi Chris,
As you may already know, there is that possibility that the tune was recorded by a house band/hired secessionists. However, there were a couple of psychedelic rock, heavy psych bands that were from Urbana, Illnois. Although a stab in the dark, at least a try...
1) "The Spoils of War" - they released a couple of albums in '69 (self titled and II). Band member Jim Cuomo moved to France and in the band "Mormos." Other members were Roger Francisco, Frank Garvey, among others.
2) "Time" - formed in '67, disbanded in '68. Released one album, "Before There Was..." I don't recall the album but have read it also contains psychedelic folk.
Hope that narrows it down.