Take a quick peek through the 'pedia. The Chasqui scout isn't two move, rather it's 1 move and all terrain as roads. No wonder they're getting the barbs so fast

. Our 2.2.1 Jav Throwers could mess them up pretty bad, since the Chasqui can't retreat. With 3 Jav Throwers already in South American, I'll keep my eyes open for a fortuitous Inca war opportunity. Their cities are on hills so I won't attack them directly, but we can pick off their non-retreating 1.1.1 Chasqui with our Javs.
If we can get up to Theology (a 2nd tier tech in the next age) we could revolt to Monarchy. Or we can go Blood Cult, which is the same as Despotism except Corruption is Problematic, and unit support is 8.8.8 (as opposed to the 2.4.8 of Monarchy). However, Blood Cult still has the Despotism tile penalty, which really stinks.
I sell the Courthouse in Chichen Itza
IT: Chichen Itza (CI) Curragh-Spear. Since it'll grow in 10, it'll complete the Spear in 4, and then build a Settler in 6. With the scarcity of food tiles around CI (and with no chance of irrigation for a LONG time), I want to preserve our pop there as best as I can.
1511 AD (1): Load up a Javelin Thrower (JT) onto the Curragh and head for the Cuban Barb camp.
The Iroquois have Code of Laws, so I give them Mapmaking for it. Net 15g from WM trades. The Iroquios aren't a threat to win on culture, as the Mounted Warrior cannot enslave.
1512 AD (2): Our JT lands in Cuba - shades of Castro's revolution. Can't drop the sci slider on Storytelling, due in 1. WM = 6g.
1513 AD (3): We are now in the Middle Ages. What to research next?

Despite our Science Advisor's suggestion, I start research on Monotheism. We need to get out of Despotism more than we need the river movement penalty eliminated. Start research @ Max.
Kill a barb archer in Cuba but no slave. Still one archer in the camp. WM = 5g.
IT: Spain starts Magellans.
1514 AD (4): Disperse the barb camp, no worker. WM = 6g.
IT: CI Spear-Settler. Copan Settler-JT. France completes Leo's. Spain cascades to Copernicus.
1515 AD (5): Settler boards Curragh and heads for Cuba. WM = 6g.
1516 AD (6): Nothing. WM = 6g.
1517 AD (7): Roads through jungle only take 3 turns to build, nice. No one will take our WM.
1518 AD (8): Can't found a city on a jungle!

Well that changes my preliminary dotmap entirely. I'm getting sick of being cut out of the WM trade, so I trade Writing to the Inca for WM + 25g. I then get the WMs off of the Aztec and Iroquois, and sell the new map to the Europeans for roughly 135g. Monotheism is out there for 275g + 12gpt, but I'll hold off and leave that choice to the next leader. I do turn off research though since we'll be buying this tech soon.
I can't see any barb camps in the fog anywhere! Damn Chasqui!
1519 AD (9): Palenque founded in Cuba on a hill. WM = 63g.
1520 AD (10): Movement. I trade our WM for 54g. Now that we're back in the WM loop, we can trade last turn's European-updated Map to the Aztecs/Inca/Iroquious, and then trade our New World map to the Europeans for gold + their ocean explored maps, and then next turn to the Aztecs etc etc . . .
The Incan city of Cuzco is ahead of us culturally (736 to 680). I establish an embassy to see why. They only produce 13 cpt (Palace, Temple, Altar) while we produce 21 cpt (we're + a ball court). They must be sacrificing their slave workers right away.
Notes for next ruler:
-Monotheism is out there for trade. I certainly would recommend it and would have done it, but I didn't want to hamstring our economy right before the end of my turns.
-We're at turn 30/150, which means we're 20% through the game. At turn 150 we'll be at 3200 culture if we don't sacrifice or build any new culture buildings. If we switch CI from a settler to a library this turn, the library will finish in 11 turns and we'll have 3,418 culture at turn 150.
-Since we desperately need sacrificial slave, I think we should start thinking about war against somebody. We have 3 JTs in South America, and 1 + 1 in production in Central America. Our starting location deprived us of easy barb slaves, since our neighbours got them all.
-None of our nearby luxuries are hooked up yet, as thus far we haven't needed them.
LK 63