If you have an FAA licence, you have to do all the exams.
That wasn't the case two years ago. I was exempt from several. It may well have changed; it frequently does down there.
There were at least two doctors in Trinidad who did FAA medicals, and I'm pretty sure they did TT medicals as well. They'd (almost) certainly do the exams concurrently, so you could theoretically update your FAA while meeting the TT requirement. I don't know what they'd charge for this. One (Stuart Millar) does TC medicals as well. Many (not me, yet) have FAA and TC certificates. You could possibly do a triple medical. I'd make sure I was in really good health before doing this, especially for the first time.