Update: nothing to report. I am convinced the 2002 proof set of Jamaica exists but that there must be extremely few in the hands of collectors.
However, I would not be surprised if a number may one day be located in a BoJ warehouse or perhaps at the Royal Mint. Really a shame as they could clear a few, although I do not know at what cost to them.
The 1984 specimen set of Jamaica also exists by report, and an Eastern European collector has one at least.
The 1984 specimen set of Barbados is also likely to exist: separately, I have gotten the PL versions of the $10, $5, $1, 25c and so almost formed one from scratch.
It is also very likely that there are some other very scarce proof sets struck by the Royal Mint for other countries (like 2004 Falklands Proof set) as well.