John,  yes, both of your piano rolls are definitely arrangements
of Zez Confrey's "Stumbling."  The second one on your site more
immediately goes into recognizable "Stumbling" phrases than the
first one does.  With the first one I was going to say, after
hearing the first 30 seconds or so of it, that it wasn't the
Confrey tune.  But it definitely is.  Both are.

Matthew Caulfield (Irondequoit, N.Y.)