(5) 1800AD Railroad finishes, we start on Assembly Line. Sirian will get to do a round of factory construction on his turn. San Roberto finishes drydock, and take a look at this!
Over ONE HUNDRED shields/turn on naval units!

(with a little overflow, of course) This is PRE-factory, and before building rails on those mine/lumbermill tiles. Absolutely astonishing. We could build a whole navy from here in a matter of turns. If Ironworks weren't being buggy, this city would get downright frightening. Since we are in infrastructure mode at the moment, Saint Bob gets set to Observatory. Our workers start workin' on the railroad! They have plenty to do.
Oh, and our expenses top 300 gold/turn for the first time. This proves that 1) we could really get a lot of benefit for being Organized here, and 2) I spend way too much time looking at the F2 Financial screen.
(6) 1805AD Vicky enters a Golden Age, making it likely she popped the free Great Scientist at Physics. Of course - I think I'd prefer having rails and factories to the freebie Great Person, all things considered. Borders expand at Seaside Dyes. And - ack! What is this foul red border intruding on our expansion plans?!
Is a war against Japan in the works for the future?

Sirian will have to decide that... (We can raise a decent little army just by dropping research and upgrading the units on former Roman Island.)
(7) 1810AD Sirian's Work Boat on endless goto finally reaches Grenada. Hooray! Now it actually has some food. Island Hopper founded on the little island that we can now reach. Under pressure from Rome's city of Setia, but we can run an Artist there thanks to Caste System and should be OK. In 3 turns when its borders expand, we'll be able to at least reach the Japanese city and take a look at it. Hopefully there will be a path from there to one of the continents!
(8) 1815AD Assembly Line finished, start research on Scientific Method. Our last monasteries are scheduled to complete just before that happens. Factories are ordered up across Cuba, si!
There are more than 20 million Cubans! Seeing as how the average AI population is around 7 million, I'd say we're ahead of the curve by a bit. And another milestone hit this turn too:
We go over 1000 beakers/turn for the first time! The first time at a sustainable rate, that is. Those observatories have really made a difference, greatly increasing our research rate. At this rate, we can get even the most expensive endgame techs in a matter of turns. We're in good shape here, no doubt about it.
(9) 1820AD Asoka proposes trading furs for wheat; I see no reason to refuse and accept. I order up about a million more factories this turn, most of which will complete during Sirian's turn. Our production will explode shortly (to be used for late-game warring? Perhaps, if we can get there!)
(10) 1825AD Scientific Method finished, Biology is the easy next choice (more food = more good!) We have three sources of oil: one in the desert on former Roman Island, one close to our new colonies in the ocean, and the final one? Where do you think it could be?
We were good enough to claim enough land to have three sources of oil on hand. But it takes some mighty powerful luck to have oil in your capital's city radius too.
Meanwhile, Island Hopper's borders have expanded and we can get a sight of that Japanese city near us:
Umm, the only reason that's a crossbow there on our part is that it was the closest unit on hand to use for scouting. Anyway, we should be able to take the city pretty easily if we want to, with only two longbows on defense. Now whether that city will let us get any further to the west is anyone's guess. Now IF we by some chance could get a Great Artist and use it in Island Hopper, we'd be able to reach Setia. Barring that though, I don't know how much further we're going to be able to do this. But Sirian may have something up his sleeve I just haven't seen yet...
Factories are under construction everywhere in our territory. Once we have those and coal plants done (or power plants of some kind), we'll have plenty of options on hand. Up to you which path to take next, Sirian.