OK, time for me to get a look at my own creation here.
Wow, I'm surprised we got this far with the islands so fast. We haven't even gotten to Astronomy either; this was all done with the sea-navigation at Engineering and the 4-move caravels. Although I guess "fast" is in relation to the tech pace, not the game date; usually by 1130 AD I'm building infantry.
I think we may as well go up to Military Tradition before shutting off research; we can get Metallurgy in 6 turns.
We've probably got quite some ways to go for domination; remember coastal water tiles count, and there's almost as many of those as there are land tiles on this map.
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Inherited turn: Change some build orders to settlers since we'll need to do a lot of filling in for domination (unless we do want to go for conquest?) Change production at home to horsemen for cavalry upgrades.
1140 AD: Tenochtitlan falls; it had three defenders left. Thanks for the great setup, Arathorn.
We trade Chemistry to England for Education and cash. They've got Banking and Astronomy, both monopolies.
Spain declares war on us! They attack and capture Lindum, on the island next door to their homeland. Looks like we've got our next target, although they're in a corner of the world where we have almost no troops.
1150 AD: Tlatelolco falls to four gallic swords and an MDI. We've got more than enough troops on Aztec Isle to finish them off.
Positioning boats to eventually evacuate Aztec Isle in the direction of Spain.
1180 AD: Teotihuacan falls, and capturing the city gives our fast units access to Texcoco. This is the first time I've used Gallics; they are pretty cool, at least once you've already invested that massive build cost.

Texcoco also falls; Aztec Isle is ours but the civ is not yet elimintated. Guess they're doing the settler-on-a-boat routine...
Also this turn, our two boats full of troops reach Spain and lands. Also also, two boats full of MDI have reached Japan, on whom we declare war this turn, and two more will arrive in another turn or two.
1190 AD: Metallurgy has come in, and we trade it plus cash to England for Astronomy! Ahh, galleons.

Bigger and faster, although they can't navigate ocean yet.
Heh. The Aztec settler landed on a mountain on an island that we control. Fortunately we have two warriors there, although it'll take a few turns to get any strong units there.
1200 AD: Our offensive at Japan actually fizzles out, with four MDI killing only one spear in Osaka, and then Japanese archers nibble us to death. I pile back onto the boats and retreat until we can get a better force there. AIs tend to build gazillions of units when cramped up on islands; the Japanese cities are going to have 4-5 spears each, and expect a dozen in Kyoto as were in Tenochtitlan.
The Aztecs plop down a city with a different settler next to Knossos, and apparently that counted as a respawn because four units jumped out of the city advancing towards ours. Well, rather than lose our city, I make peace. We can get troops in position and kill them in 20 turns. That also ends our war weariness.
1210 AD: Positioning. Don't ask why Entremont doesn't have a harbor anymore; I screwed up.
1220 AD: We land at Madrid with 11 MDI, one Gallic, and two muskets. I hope it's enough.
1230 AD: Let's count the spears (all regulars) in Madrid. One, two, three - and that's it? I brought a dozen MDIs for that? Well, we now own the Spanish capital.

I pass off in 1230 AD with most of the rest of the units unmoved. Next leader can take the stacks around Agedincium-Monguntiacum Island down to Japan now, or wait to upgrade those horses to cavalry.
I think we should go for conquest rather than domination. It's cleaner; settling in all the little crannies and waiting for temple expansions is a bit of a pain. I was worried about one-square islands, but we own one of them, and we have cities within two squares of two more (both southeast of Spain) so I don't think the AI will settle on them (and it would've by now if it were going to do so.) I can't see any more one-square islands; I don't really recall if there are any more on the map.
Military Tradition is due in 4-5 turns and we can go nuts with cavalry after that. England will have muskets, so we'll want the cavalry to beat that. We should have enough troops at Spain already to finish taking them out.
http://www.civfanatics.net/uploads4/th4-1230ad.zip