The Edison Phonograph Monthly was a periodical published between 1903 and 1916 in New York by The National Phonographic Company. The full set of EPMs can be viewed at The Internet Archive.
In the introduction to the very first issue in March 1903, the Company wrote that it believed:
…that some means of keeping in closer touch with the Jobbers and Dealers has become a necessity. The Company also believes that the trade will at once recognize the advantage of a medium that shall at least monthly keep it informed concerning Phonographs and Records. To keep the trade advised on these subjects will be the sole aim of the MONTHLY. It will take the place of the Monthly Advance List of New Records, which will no longer be issued in its former shape… The MONTHLY will keep the trade posted on changes made in the Phonograph from time to time, will give new goods listed or dropped from the list, will note the progress of new catalogues being gotten up… In a word, it will endeavour to further the sale of Phonographs and Records…
The introduction went on to request feedback in the form of criticism and suggestions from its recipients, in particular wanting to know what subjects should be touched upon each month.
For us, the important aspects here are the lists of new goods and goods dropped (new releases and deleted titles in our case).
My task, then, was to search through the monthly issues, trying to find any references to Carmen Carmela (by anyone).
(There remains, of course, a possibility that the number was recorded still earlier and that it then appeared on the so-called Monthly Advance List of New Records, but I have found no evidence of an earlier recording in any other list that I have. If you have any evidence of an earlier recording, please contact me.)
My search took me to the following numbers of Edison Phonograph Monthly