I have made the Trip from Seattle to Florida, basically 2 that way, and one Puerto Rico to Long Beach. The boats were single engine motor sailors, which would go 8 knots under power and 8 knots under sail. My range under power was 3000 miles. The boat cited is closer to 1.000 miles under power on a good day.
Range under power not sufficient
Boat not made or equipped for weather you may encounter many places along the way.
You need 4 line handlers, plus the skipper (he is not a line handler).
I have seen boats like the Nordhavns make this trip, also Seaton trawler, a Defever passage maker (closest to your cited boat, but with a lot more fuel,
Shutters for the windows/ if broken I Wirld of hurt.
I have seen winds of 90 knots on this route. How would that boat stand up to 90 knots of wind? And the seas which come with this?
You have to have the fuel tanks cleaned (Polished with all old fuel removed, tanks rinsed out and refilled with filtered diesel. There are a lot of issues on a single motor vessel. With my motor sailor, they are decent sailing boats and I had made several 24 hour passages which were just over 200 mies, With sails I had an auxiliary source of sailing-at getting somewhere. I you had an unfixable engine issue pretty good chance you would loose the boat, AMVER might pick you up, but they are not going to salvage the boat--sink it, or let is sink.
Don;t do it on its own bottom. You might make it--maybe not.
A neighbor in Calif. took a Bertum 55' sport fisher (twin engines) down from FL, thru Mona Passage, the Canal and then strait up to Long Beach. He said he would never do that trip again, He had carried extra fuel in bladder tanks and barrels.
For a smaller boat the route is best thru the Western Caribbean (Belize, Honduras, Mexico and then to your preferences in FL. We went from Yucatan to the Keys, and to Pensacola. Slightly different routes. But we had the range to go straight. Going back we stopped only at Panama to make the transit. We had met with the chief pilot and he gave us next day passage, if we would go from the Mere flores lock after dark without an advisor. We did it, but with about 6 knots of current behind us, we were flying thru the Bridges of the Americas, and when we turned into Balboa YC, I had reserved a mooring right at the edge of the Chanel, and it was red line to buck the current and pickup the mooring. I probably would not do that again. (Boat was already admeasured, and we had volunteer crew lined up; plus I already had the prescribed size of lines. We did top off fuel at Acapulco, not even staying overnight, or checking in.
-- or if it is a different boat, please tell us. 
