A copy of Gillette's recording is available at Michigan State University
in the Vincent Voice Library, where it appears to have been digitized
(not available online, however, as far as I can tell). To get more
information about their copy, here is the direct link to the
bibliographic record:

http://vvl.lib.msu.edu/record.cfm?recordid=7456

Jim Edstrom, Harper College, Palatine, Illinois