In the past 20+ years I have been living here, nothing like this has been done on the island. And it would be my educated guess that no one attempted it back when Capt lived here in the 70's and early 80's.

The cost of the weather ballons (if you would even be able to obtain them without a permit) and helium would make this a rather costly stunt. Let alone the massive fines and probably jail time for pulling such a "stunt". And should something go wrong, you could literally land (fall) in an area that would be completely out of range of any human intervention.

So to paraphrase the old "dont try this at home" line, dont try this in Jamaica.