Well, now look at this page from the University of Florida Library that Dale Rose linked me to: click here. Here's what it says:
Titus, John Henry, The Face on the Bar Room Floor, [original] Ts., 1 p., dated 1872 & signed. Revision attributed to Hugh Antoine d' Arcy in 1887; photocopy of printing in Parlour Poetry: A Casquet of Gems ; pp. 231-3; w/ short bio.Kinda puts a new light on things, doesn't it? Now is there anybody near Gainesville who wants to go take a look and transcribe the original for us?
Actually, Dover has the Turner book in print. Anybody got a copy? Looks like I've got another book to order.