I've plied the Caribbean doing deliveries for several years- a couple out of the Western Carib via Yucatan Channel, cross Gulf to Galveston. So, while there are others more knowledgable I'll contribute my experience to open the dialogue. From the phrasing of your routing question I assume that you are on the Gulf Coast side of Florida. If so, then you have 2 possible routings to Trinidad- SE in deep water North of the Caribbean Islands or SW across the Gulf to the Cuban edge of the Yucahan Channel through the Western Carib. Neither of these routes would be a picnic.
There is a "sort of" window that could allow the North of Islands passage. The pilot charts show that from December through March the NE Trades blow more consistently from the NE throughout the entire Caribbean and don't become essentially Easterly below 20 degrees. I had a Bermuda to Antigua delivery this past January and found that the winds stayed fairly consistent out of the NE...without getting an Easterly component once we got near the islands. However, I and a lot of sailors are saying that things have changed with global warming or at least warmer waters South of Bermuda and that the historical basis upon which the pilot charts rest may not be gospel now. To get a handle as to what has actually occurred at this time of year go to the QuikSCAT satellite data archieves for the last couple of years. QuikSCAT provides global surface wind data and the archieves go back to 2000. When I prepare for a voyage in either a new area or a time of year outside of my experience I'll study the daily wind maps starting 15 days before my scheduled departure and 15 days after predicted arrival. I'll do the most recent year and the year before (so your study would center around March 2008 and 2007). While time consuming looking a two year's data and getting the same picture will give you comfort that it's probably not a single year wind anomoly. Since wind systems don't shift on a exact date every year the wide window (15 days + / -) gives you more information for the time period your transiting the area.
Staying on the SE route the major currents are against you. The "Antilles Current (alla Jimmy Cornell, but I've seen it called by other names) would be dead on your nose. I have been told and read that it is predominantly centered over the Puerto Rican Trench. But, candidly I've never had it show up on a GPS course-over-ground shift as I've crossed the Trench plenty. If it's real and significant you could go far enough offshore (North of the Trench) to avoid it. However, I have found over by the US and British VI's a strong coastal East setting counter-current that would help you. I have no knowledge if it exists on the North shore of Cuba and Puerto Rico. Perhaps some sailors from those areas could give some input.
The route through the Yucatan Channel would be very long, but does have a couple of rest-stops if the alleged steadier NE's of December- March pentitrate into the Western and Central Carib. You'd have to enter the Carib from the Gulf close to the Cuban shore (I forget the name of that Cape) to pick up the counter-current. Then, I'd stay nearer to Cuba's South side than the center of the Carib until I could easily reach Grand Caymen. Then you could do a 3-4 passage to the North shore of Jamaica (Montego Bay or the newer cruise ship ports to the East). Here's where you might find yourself in a bit of a box. If the NE's are really steady in December-March you might not be able to get North through the Windward or Mona passes, or around the SE tip of Puerto Rico. Instead you have to sail to towards the Windward Islands to await the Easterlies of April-May to make your Northing. Again, I hope this dialogue attracts some local sailors from these areas to give some local knowledge.
Finally, I've never read the book you mention. But going back to something I've said earlier- warmer waters are distorting historical wind and weather patterns- I'm pretty sure that I'd discount guides based upon long history.
Hopefully, this response will spark some discussion. Maybe some Gulf of Mexico sailors will jump in. Somebody surely has sailed from your neighborhood to Tortola.