Wow Buckeye, what an interesting dream! You have received a lot of replies and they all make some sense to me. Just driving solo down to Honduras would be a real adventure, if not potentially dangerous. Sailing there from FL is certainly a potentially more intriguing idea than driving but not without its own pitfalls. As to how you handle Cuba and the prevalent currents in the Caribbean I leave up to the experts. Sometimes the shortest route is not always 'the best' route which is why most sailboats come from Europe in the southern northern latitudes and go back across in the north.
As far as being on the ocean for a few days time I can comment having recently gone around 400 nm from Tortola to the Turks & Caicos Islands. I had no ocean cruising experience but went with an experienced captain on a proven 50+' sailboat and sailing all night on the ocean is not all that romantic , and we had 'good' weather. Since you are in OH can you get out for several days and nights straight on Lake Erie (or have you already done this)? When the horizon disappears at night and there is shipping nearby it is not really a safe proposition. We had every safety feature on the sailboat I was on: Radar, Sat-phone, autopilot, chart plotter, life raft, harnesses, tethers etc, etc. I would resist going offshore without any of this stuff that can cost 20K alone. Heck, I would not consider doing this trip by myself even on the 50 footer I was on, so more power to you if you can pull it off.
Jimmy Cornell's book 'World Cruising Routes' talks about the Gulf of Mexico during the winter months (Dec - Apr). He mentions a prevailing NE wind with strong 'northers' that last 2 days and sweep the region nearly weekly that can gust up to 60 knots. I may be chicken-ship but I would rather watch that from safely from shore.
Here is a neat link that has a web viewable chart of the area in question: NOAA
Good luck with your dream.