From the time of my last spoiler, I researched Compass -> Alphabet -> Polytheism -> Literature. I completed the Great Library to give me a research boost. I also founded Alexandria South of Thebes in 475 AD, near the neck of the peninsula to pick up spices, iron, and rice. I later founded Pi-Ramses (560 AD) and Giza (980 AD) on the west and east coast of the middle area. I next researched Mathematics->Currency->Calendar->Machinery-> Optics. Just before Optics (~1000 AD,) I met Washinton's caravel. When I saw he was lacking philosophy, I used a Great Person to discover the tech for trading purposes.
In the previous spoiler I wrote up, I mentioned that I found land just off the NE corner of the island. My galleys explored it and found an empty island.

There was a goody hut, which gave me angry barb warriors. There was also marble, copper, and furs on the island, so I later settled 2 cities there (Byblos in 1260 AD and Armana in 1280.)
I discovered Optics in 1100 AD and sent 3 caravels out exploring. It didn't take me long to meet Mali, Rome, England, China, and the Mongols (I had already met the Americans.) I successfully circumnavigated the world in 1290 AD. When I met the other civs, Caesar was 1st in score, Qui (China) 2nd, Washington 3rd, I was 4th, followed by Mansa Musa, Elizabeth, and Mongolia. There seemed to be 2 factions among the AI: Washington, Mansa Musa, and Elizabeth vs. Qui, Caesar, and Khan. Since Washington and Mansa Musa were the most advanced and had the most techs to offer, I traded techs with them and got close to tech parity (2 techs behind Washington, even with everyone else.)
In hindsight, my choice of trading partners might not have been that great. Elizabeth and Mansa were willing to trade techs, at least up until the space race, but Washington got tight and wouldn't trade me a tech until pretty much every other AI had it, if then. It left me in a situation of chasing after him tech-wise for the entire game. The all-too-familiar pattern went as follows: I'd start researching a tech nobody else had. A couple of turns before I finished it, Washington would discover it and trade it to Victoria and Mansa Musa, leaving me holding a tech I didn't need that badly and couldn't trade with anyone (Caesar and Qui refused to trade techs the entire game.) This happened at least 6 times during the course of the game, so I finally gave up and had to do the majority of research myself.
After Optics, I went for Civil Service (1180 AD) and switched to Bureaucracy. Hanno (Great Merchant) was born in 1200 AD and I used him to discover paper. Rather than trying Education->Liberalism and taking Astronomy as a free tech I chose to research Astronomy directly becuase it was ~ 20 turns faster that way. Washington discovered Liberalism in 1410 and I discovered Astronomy in 1450, so I think he would have beaten me either way. I did manage to trade Astronomy for Education. I picked up Nationalism shortly after and built the Taj Mahal, which set off a Golden Age filled with University building.
At this point, I had to seriously assess my chances of winning. Being isolated, the only reason I had been able to stay close to the AI's in tech was by building a few crucial wonders (Colossus, Great Lighthouse/Library, Pyramids) and neglecting my military. This, coupled with a serious lack of hammers in most of my cities, pretty much ruled out conquest/domination. It was an ideal spot for a cultural victory, unfortunately, I didn't get my first religion until 1490, so that also would have been extremely difficult. I chose to focus on research and see if I couldn't pull out a space/Diplomatic victory.
Along the way, Caesar founded a city on the very souther tip of my continent to claim the sheep there. Unfortunately for him, my culture from nearby cities soon engulfed his city and left him with only sea tiles. I guess he didn't like that, and in 1760 AD, he landed a stack of knights and riflemen in Arpinum and declared war. Luckily, I had been strengthening my military in anticipation of such an attack. I was able to kill off his stack and capture Arpinum in 1780 AD. I built several frigates and sent them west to blocade his 2 seaports. I was also able to bribe Mansa Musa to go to war with Caesar. After I sank 2 frigate and 2 galleons full of cavalry/cannons headed my way, he agreed to peace and paid me 400g for my trouble.
During the war, Caesar fell from 1st to about 4th in score. I moved up to first, Washington to 2nd, Qin to 3rd. It was bad news because it meant that my 'buddy' Washington would be the other candidate for UN secretary general. Since Qin and Caesar hated both of us (Mongolia had been destroyed by this point) they could be counted on to abstain, and Washington would vote for himself, making the chances of a UN victory slim.
I pretty much spent the last part of the game chasing Washington's tail. I got close a few times, but I could never seem to quite catch up. He was about 2 steps ahead of me for the entire space race. I tried a bit of a gamble to see if I could catch up. After I researched rocketry, I went for Radio and Fission and managed to trade them to Mansa for plastics. I then researched Computers -> Robotics -> Fiber Optics -> Fusion. My plan was to start building the Space Elevator (Robotics) and the Internet (Fiber Optics), score a great engineer from fusion, use the Gr. Eng to finish the Space Elevator, finish the internet to catch up on techs, and see if I could outrun Washington to the spaceship. Unfortunately, he beat me to fusion by 1, and used *his* GE to finish the Space Elevator. I did manage to finish the internet and it brought me Satellites, Composites, Ecology, Fascism, and Mass Media. At that point, I lacked only genetics, but to my horror I saw in the tech screen Washington had just gotten it. With a 7-turn lead on the final part, I knew the game was lost, but I decided to play it out anyway. Washington launched in 1970. I was 6 turns from finishing my final part.
Final results:
Space Ship loss, 1970 AD. Final score: 5474, In-Game: 3911, Rank: Nero.
Looking at the date, I'm surprised it was such a close race. In my previous experiences, the AI usually wins SS in the early 20th century. I'm sure the game was winnable if I had made different decisions early-on. Siding with the Washington/Mansa/Elizabeth faction meant I had nobody to bribe into a war against Washington to slow his research pace. Also, that alliance was strange. Somehow, he was close enough with them to trade techs, but far enough apart to give me negative modifiers for signing defense pacts with Mansa/Elizabeth. He definitely wasn't a friend of Qin or Caesar though.
A curious note about the Space Elevator: I decided to reload an earlier game and try the ending again. I beat Washington to fusion and scored a great engineer that I used to rush the Space Elevator. He won even faster (1968.) My guess is either that Washington used the money from his project to research faster, or else he was tying up one of his big production cities on the SE and was able to build the last parts faster by freeing it up.
Anyway, thanks for the fun start!