There has been an interesting TV series on the history of the Royal Navy done by the BBC where a lot of this history was covered.
The "New World" involving North America and the West Indies was evolving during this period and because of the climate, the production of sugar and various other crops were of commercial interest. Since cane farming is labour intensive they started using slaves. British dominance prompted the French to up their game strategically which led to the British increasing the size of the Royal Navy. This steadily progressed until the Royal Navy in itself was a major industry. The dominance of the Royal Navy made Britain a super power through 150 years.
It seems that Bristol was the major trade port. Slaving along with sugar and tobacco generated enormous wealth during this period.
It would be difficult to establish movements of people during this period because few records were kept. There were some census records for the West Indies but the only Oates' recorded about this time were George Oates and family in Barbados. There is no record of them having a son named James in these records. Also difficult to establish with any certainty that a given person is the person that migrated. I am not sure if anyone has done any detailed research on the Yorkshire families. I have focussed on the Cornwall families because those are my origins. The research required is quite daunting because it requires cross referencing individuals against baptism and marriage records.