I hear they Paulownias have a rep as invasive in the SE US; here in Oregon
it's no problem. They are in the Bignonia family, so they are related to
catalpa. Ther.e are a bunch of species in China, so there ought to be one
that'll grow in Jamaica.
Sposedly in Japan you plant one when a daughter is born, to make her dowry
chest from. That's quick. Root cuttings are an easy propagation method.
I've seen Chinese papers on interplanting with bamboo; now THAT would be
good for Carolina hog waste!