I don't know if Jamaica would be able to retain its independence. Haiti was able to become and stay independent because France physically couldn't project enough power to reconquer Haiti if it wanted to. Haiti gained independence in the context of the Napoleonic Wars, where France didn't have the ability or resources to send an expedition to Hispaniola with near constant British blockades. Jamaica, on the other hand, would be an island country declaring independence from the world's foremost naval power. Sounds a bit doomed to me.
Also Boyer couldn't send any military help, he could barely project power into the interior of Haiti.