Do'able, H27 to Islands
The H27 is a solid boat and should do fine with the right weather. Work your way down to Florida the safest way possible. Then take the shortest route over to Grand Bahama island, about sixty miles I think. You are crossing the Gulf Stream so conditions have to be right and steady. You do not want to encounter any winds from the north during the passage. You could clear customs at the west end then proceed north of the island over to the Abaco channel. Or you could sail directly to the Abaco channel and check in at Marsh Harbour.
I was amazed at how calm and shallow it was north of the island after leaving the Gulf Stream. You want good charts for the entire trip. We'll assume the crew is qualified and the boat is ocean ready.