Try the
Guttag Catalogue. There is a number of those S.D. countermarks under Santo Domingo. I don't know whether anything is said in the intro to Santo Domingo about them. (Unfortunately, the PDF is of rather poor quality.)
I would be interested to know what auction catalogue you got item #1260 from.
I doubt that they would be official countermarks. There seem to be too many varieties of punches, most if not all done in an amateurish way. Whether there are any good numismatic studies out there that link them with certainty to Santo Domingo I don't know.
A nice case to keep in mind is that of the "I B" countermarks, mostly found on early US large cents. For quite some time it was believed "I B" meant "Islas Barbados", and this was actually raising the value of those coins quite a lot because of the popularity of Caribbean countermarks. But we now know it is a private countermark originating in the US or Canada, as Greg Brunk has shown.
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