A good reference for this is Jimmy Cornell's "World Cruising Routes": http://www.amazon.com/World-Cruising.../dp/007140869X
Noonsite is also a good reference for info on places you might stop at: http://www.noonsite.com/Countries/TurksCaicos
Also of concern is the normal prevailing winds in January which I believe are from the E/NE. There is a special map that shows prevailing winds by month (can't find a link for this). The biggest concern would likely be how/when to cross the Gulf Stream as it is known to be rough (read miserable) when the winds are out of the north, against the current.
NOAA has a product called 'Radiofax charts' for the Caribbean which can be useful for checking wind/wave action where you will be heading: http://weather.noaa.gov/fax/gulf.shtml
One thing to be said for the northern route Faster shows in his chart is that you would be able to stop at various Bahamian islands to rest and recoup. This route is also farther from Haiti and Cuba, if you are worried about boat people finding you out on the ocean. The downside is that you'd more likely get to FL around Palm Beach or further north.
I've only gone from Tortola to Turks & Caicos by boat and that was a 3 day ride. From there you could mostly do long day sails to your next anchorage. Final hop across the Gulf Stream is nearly a full days sail.
The southern route may be slightly more direct but you might encounter more shipping.
The good news is that heading west is usually considered to be 'downhill' (eg., with the waves). Heading east to the Caribbean is called the 'thorny path' or some such as it is all 'up hill'.