For a fairly detailed history of recent (last 60 years or so) history of the song's travels see the post "Subject: RE: ADD:Dunne Song /Mr. Done and Over Done and Under.. From: GUEST,Frank Jeal. Date: 17 May 10 - 12:50 PM" on the thread "http://www.mudcat.org/thread.cfm?threadid=4548"
(Sorry my computer doesn't understand the instructions about inserting links.)