A little update.
The other civs in this game were Japan, Dutch, Austria, Ethiopia and the Celts. Since everyone except the Dutch hated me, I decided that I was going to wipe them all out rather than go for a science victory as initially intended. Japan fell first because they started settling islands I wanted. Austria (the strongest civ at the time) became the testing ground for my new Ships of the Line and Privateers. They performed exceptionally well, every city was on the coast, I've never even had a single land unit enter combat. I've just obliterated the Celts, the Dutch are next now since they've stopped being my friend and refuse to trade luxuries reasonably.
Now that I have Ironclads and the Dutch are barely in the Rennaisance they should fall very quickly, thereafter it'll just be me and Hail Selassie.
I've got to tell you, It is incredibly easy to travel the world sacking capitals with a fleet like mine which has about 6-7 ranged ships and 6 melee ships like Privateers.