] Was Antigua at the time JA wrote Mansfield Park (around 1812-14) predominantly slave-owning or was it not?
I wish this larger subject was susceptible to such an easy answer.
Jason makes a lot of good points, but is wrong on two - Antigua would have been instantly recognisable to most of Jane Austen's readers, not least because of the associations with Nelson and with the Duke of Clarence (whose house is now the residence of the current President) and was at the very centre of the naval action. Yes, other place were fought over; St. Lucia springs to mind, but a bit like saying London and Portsmouth weren't really involved in the Second World War because they didn't change hands.
There were sugar plantations, although other islands were increasingly more successful, and other agriculture, and much activity would have evolved to support the dockyard and barracks. There certainly there were slaves, and indentured servants and free laborers.
Notably at the dockyard... At the yard, there were skilled resident tradesman and artificers, many of them black. They were employed for the repair of ships. The Bosun was in charge of laborers who were Africans, bought by the Navy and known as the King's Negroes. Their responsibilities included the building and maintenance of facilities and wharves, the warping of ships into the harbor and the preparation work prior to careening.
As far as the later history it is strikingly like Malta in our times - too dependent on the Navy, eager to be independent, and then free and poor.
So why did Jane Austen choose Antigua - I still say because she knew about it and her readers would also - if she had wanted to make a point about slavery she could easily have chosen another island, perhaps Jamaica. Now there's an island we could argue about !!!