You're actually doing what's supposed to be done next although the game doesn't actually tell you 😵
Your next step once you gain the loyalty of the "free captains" is to systematically take control of every town on the map.
Doing this requires a free officer (one not assigned to a post) and successfully destroying the town fort (fire your cannons on it til it's guns die) then kill the guards in town. Once this is done you get a choice of "Pillage" "Destroy" or "Capture" (if capture is unselectable you needed to have that spare officer) select the latter and the town's yours.
Although they say it doesn't have an official ending the main quest ends when you've captured all the towns in the carribean for Libertaria.