You are asking some questions that cannot be answered without a thesis level of study of old papers, notebooks, and locally issued recordings that are not available outside of a handful of collectors.
Mento music is perhaps the best source we have, collector-based, but field research either has not been done or is buried in theses in university holdings. Like many old UK songs, the exact origins may be lost.

Perhaps you should consider origins of mento-Jamaican folk as a graduate college thesis. It wouold involve on site investigation and search for old comments and recollections in reports, papers, memories.

Here is a link to a Gleaner article which has the same information on Slim & Sam* as that on the large mentomusic site:
http://jamaica-gleaner.com/gleaner/20030629/arts/arts1.html
It could be a cover of an earlier recording, or collected by them.

Look up *Sam Manning and Lionel Belasco at mentomusic.
I hadn't seen the Jazz Oracle catalogue before this morning. It shows a circa Dec. 30, 1925 date for a recording of "Sly Mongoose," attributed to Lionel Belasco. Two Sam Manning cds are listed.

http://www.jazzoracle.com/catalogue/BDW_8028.asp
also
http://www.jazzoracle.com/catalogue/BDW_8029.asp