At the USNavy site I gave above - look for "Caribbean" and click on it. Then scroll down to find currents and click on the Gulf of Mexico currents - You will end up somewhere with this url: https://oceanography.navy.mil/legacy/web/cg...40/145/0-0-17/0
These charts show the most current data for the Gulf of Mexico down to Honduras.
The NOAA Atlantic Pilot charts page 3 also shows historical currents and speeds for the months you are interested. See: http://pollux.nss.nima.mil/pubs/pubs_j_apc_list.html
October is shown as a really good month, better than November "historically". But remember that the "end of the season" hurricanes start in the western Caribbean during those months. September is as good as November, but December starts to get nasty according to the historical data.
On a large chart it seems the most direct route is north to the windward passage then west to Miami - about 1135 nm. But heading NNW to Cabo San Antonio (Cuba's western tip) then following the "stream" east to Key West is about 1200nm and probably faster due to the currents helping. Still you are looking at 10+ days undersail and can expect a few weather encounters.