My contribution won't be worth a lot,
but this does put me in mind of a thread I started.
My subject was the popular song "Eibhlín a rúin,"
also known as "Eileen Aroon."

And what catches my attention, is that
"Eileen Aroon," as is claimed of your song,
was popular during the same time period,
also with people who had no Gaelic whatever.
You can see the proof of this in documentation from the 17th and 18th centuries.
And this documentation is attested to in Mudcat's Digital Traditions,
where there are something like SEVEN Eileen or Aileen Aroons, and a number of them
are much the same as your "callin o custure me," written out phonetically as though with Italian vowels and consonants.

The song presented in the OP is entirely unknown to me.
But after what can be observed of "Eileen Aroon,"
it sounds like you are on to something.