Talking of "Jamaican Song and Story", I found the Porject Gutenberg ebook, and found another song which is related/could be a variant of "Big Big Sambo Gyal". It is called "Bungo Moolatta" and has the "han' full a ring" line:
CXXVII.

Schottische.

Bungo Moolatta, Bungo Moolatta,
Who dé go married you?
You hand full a ring an' you can't do a t'ing,
Who dé go married you?
Me give you me shirt fe wash,
You burn up me shirt with iron,
You hand full a ring an' you can't do a t'ing,
Who dé go married you?
-Walter Jekyll, Jamaican Song and Story