I felt compelled to do that, because I got all the boring set-up turns and now Gator gets all the exciting ones. I am highly suspicious that the fix was in with this player order.
Summary: Oracle due next turn. AIs are now officially toasted.
1600: change Machu from granary to barracks. Get Masonry
1560: Start CoL, due in 16
1520: Cuzco gets Settler, start worker. Hire 2 scientists and CoL is now due in 11 turns.
1440: Found Ollyantambo (aka Fish Fry) and start a work boat. Will explain that choice later. Workers are building cottages to be used by the tiny cities of Tiwanaku and Ollyantambo while they are waiting for their borders to expand.
1400: Switch 3 cities to work coast tiles and get COL 2 turns sooner.
1280: put a couple of citizens back to work on high hammer tiles. COL still due in 3. Machu reaches the happiness limit.
1200: Machu gets barracks, st. Settler to make use of all Machu's extra food from the pig and FPs. MM cities so that CoL is due in exactly 1 turn. Chop completes, which will complete the Oracle next turn and send a big overflow into a workboat.
The reason I tried to keep our cities building units like workboats, workers and settlers is because I think our next tech should be Monotheism. That will enable us to spread our religion with Missionaries via Organized Religion (remember, we should NOT research Meditation or trade for it).
I like to build things in waves when possible: units and such prior to Organized religion, buildings after. We would be better off building our structures after we are in that civic due to the 25% hammer bonus for buildings. This would also be a great time to chop down a few more forests to get Libraries built.
After Mono, I would get Math, but Monarchy or IW are certainly viable options as well. I would chose math because it would enable us to build the Hanging Gardens in Tiwanaku and start generating Great Engineer points to add to our prophet points. If we generate an Engineer in time to research Machinery or Engineering for us, it will knock quite a few turns off our victory date.
In the long term, I think the four cities we now have should get Libraries, along with the city that we found in the dyes. After that, building any libraries would be a waste of our time. The game won't last long enough for us to see the benefit of any additional libraries, except perhaps in a heavily cottaged AI city or three that we capture. Almost every city, however, will eventually need a courthouse and a barracks.
For Gator:
The worker in Machu was on his way to build a cottage on a grass tile shared by Cuzco and Machu, but perhaps you will think of a better job for him.
Adam jumped NE to the forest hill in order to let a barb attack him and die. I would move him back SE to the hill after that (in hopes that the dreamed-of barb city will still appear for us)
Several cities should be MMed to hammers or cottages from the coast tiles as you see fit after Code. They are only working all that commerce in order get Code next turn.
Be very careful with Machu and Cuzco. After they build their settler and worker, they will grow very quickly. I wouldn't allow them to grow unless you can get religion into them quickly and increase the happiness limit.
So I got all the boring turns and you get all the good ones.

My only consolation is that, if you revolt (as you should), you will miss getting to build the academy by one turn.
Speaking of revolts, I personally would revolt to bureaucracy and caste system, then follow that with Confucianism. I am willing to try the slavery route though if you guys would like.
There are two reasons I like Caste System better: 1) we can expand borders in our cities quickly by running an artist for 3 turns, which allows us to ignore culture buildings and funnel those shields to the military where we want them, and 2) we can run merchants. Merchants will allow us to use our bureaucratic/academy captol more effectively. We don't want to lower our science slider if all all possible, because the library/academy combo multiplies our research by a percentage. So the lower the science slider goes, the less value we get from the science buildings in our capitol.
Edit: Hmmm, forgot something important:
The Save