"But just to have the freedom to roam up and down, stop when drawn in, leave when ready..."

Most drivers will do that for you, plus they know the roads and the runnings. Hire them for the day and they'll take you wherever you want to go; it may not even cost more than a rental and you may actually enjoy it more. Personally I would never consider driving a car in Jamaica, it's not like home for sure, and add to that the fact that they drive on the other side of the road...