Quoting Morrison's ch. 8 note:

24. The 'Streights' are not, as is so often thought, "the Straits of Gibraltar," but rather, the "Straits of Florida," which extend from the Florida Keys in the north to Cuba in the south, and connect the Gulf of Mexico with the Atlantic Ocean (Harris, 79).

Harris, Jocelyn, A Revolution Almost Beyond Expression: Jane Austen's "Persuasion." New-ark: University of Delware Press, 2007.

In this context, never going beyond the Streights, would mean never going into the Gulf, to central or South America, or to any of the islands south of Cuba.

As for never having heard this area called the Straits of Anything, well, neither have I, but I had not heard of Alaska being called Russian America until I saw a clip of Lost in Austen. Wikipedia does have a short article about the Straits of Florida. Currently, indeed, the West Indies (usually called the Caribbean now, although the other name is still in use) includes the Bahamas according to Wikipedia, no matter what Mrs. Croft says.

Really, if she went to Gibraltar without going past the Strait of Gibraltar (note the singular), I would be hard-pressed to say how, since Gibraltar by current maps seems to be on the other side of the Strait. I would say that she meant never went beyond Gibraltar, if I were to read it as referring to that Strait.

I never even questioned this being the Strait(s) of Gibraltar, until two experts contradicted each other. (Everybody know the old joke about a guy with a watch always knowing what time it is, and the guy with two watches never being quite sure?) Now, I am wondering what the two base their conclusions on, so I can make up my own mind.