Both "No Regrets" and the instrumental "Shreveport Sunday"(?) fit Open C. (CGCGCE) So much so that I usually use a chunk of the latter as an intro and outro to the song.

Listening to the record, I'm fairly sure that is the way Tom Rush played it. I've always sung "Circle Game" in straight EADGBE, probably because the first version of it I heard was by the Ian Campbell Group. Must try it in Open C some day.