I have no record of the Comet 4s (introduced late 1958) serving any North Atlantic route other than the pioneering days to New York with a fuel stop. They were Africa/Asia medium-haul aircraft for routes with lots of stops.
Routing in the 1960s to Barbados etc was through either Bermuda or New York. This latter was used a lot. The VC10/707 split to the Caribbean varied over time but it was common to use the 707 through Bermuda and the VC10 through New York.
Before the 707 came along it was indeed the Stratocruiser. The routing to the Eastern Caribbean in 1956 was London-Gander-Montreal-Bermuda-Barbados-Port of Spain, likewise on from Bermuda to Jamaica. Some flights skipped Montreal, which does indeed seem an awful long way round.