I'm finished too! I had a good game this month, the approach I took turned out very well.
In summary, with the advantage of hindsight, the key elements of the game as I played it were:
1) Careful management of the start position to squeeze every possible crumb from it.
2) A long initial build up to produce as many Horsemen as possible with the available resources.
3) Built a number of temples early to get a cultural lead. This was important because I wanted to capture towns later, not raze them. Razing requires settlers, and resources seemed too limited to produce them. High culture would allow capturing instead of razing.
4) Built up a big cash reserve. No research after some initial techs. Early exploration and carefully managed trade between the other tribes supplemented the income produced while not-researching. Buying slightly old techs was cheap (often just traded maps.)
5) As soon as other tribes had learned the prerequisites for Chivalry I bought those and researched Chivalry at top speed. Then I used the big cash reserve I'd built to upgrade the previous Horsemen production into Knights. I.e. I used the money to leverage the 30-shield Horsemen into 70-shield Knights, effectively doubling military production up to that date.
6) Sent the Knights on a Crusade before anyone could prepare for them. American culture far overshadowed everyone but Egypt. The Knights swept through one tribe after another, capturing towns. They greatly exceeded my expectations! After each victory, enough remained (with meager additions from the homeland) to continue the crusade to another tribe's land.
At the start of the game I produced some Swordsmen and Horsemen, and waged a war which nearly eliminated France. Losses during that war were high, especially when compared with early America's production. I didn't want to attack Russia the same way, losses would be even higher. That's when I started working on the approach which eventually developed as described above.
In the Crusade, I drove each tribe out of its homeland, giving them peace only when their government had fled to an island. First Russia, then Greece, then Japan, capturing all of their towns. Finally the crusade continued even to Egypt, razing the towns there because of their high culture. When the crusade finally ended after Egypt, I decided to play the game out for a cultural win. The date at that time was already well past a time when an early win bonus could outweigh playing it out.
Although the start position was very resource poor, the good thing about this map in the long run was that no tribe had a good start. France, Russia, and Egypt had slightly better starts than America but far from good ones. Japan had nice land but it needed irrigation and they had no water. Greece had a very nice bit of land but they developed it slowly. I suspect that their land was initially all jungle and that this delayed their start. If Greece were allowed time to build I think they could become a very strong rival on this map.
The rest of this note is a more detailed diary in case anyone is interested:
I settled Washington on the incense NW of the start position.
After the first bit of scouting I concluded that the start was very resource poor. Shield production would never be high. The best initial build seemed to me to be 3 towns south and east of Washington and 5 hill towns. (I actually ended up building 6, adding a forest town NE of the hills.) The towns near Washington would be on the 3 points of land. The one south of Washington would require a temple before it could utilize the whales. The hill towns would each reach a maximum size of two, working two hill tiles.
Building this many towns would be difficult because of our limited food supply. So the first thing I built in Washington was a granary. Micro-management of the 10 tiles which could produce 2 food each, between the four southern towns, was important for a long time.
I rushed improvements at critical times. When a town's happiness and current task permitted, and all food tiles were fully utilized (the town was not growing) I rushed something. Temples. (I decided fairly early that eventually capturing rival towns would be important. There was little capacity for building settlers for a raze and replace approach. So I built some early temples to get a culture lead.) Barracks in the hill towns. (A barracks costs 40 shields. A rush gets 39. The 2nd tile worked by a hill town got 20 shields in 20 turns. A size 1 hill town regrows to size 2 in 20 turns. So rushing a barracks at the right instant saves 19 shields.)
The scout got a settler from a goody hut east of France. The land there was barren so I sent the settler home to help the buildup there.
My research began with Alphabet. (I started on the sea-faring research path before realizing we were not alone on our land.) After Alphabet I switched to Bronze Working because the French were nearby, defense might be important. After that Ceremonial Burial because I wanted temples. Then I traded for Warrior Code and researched Iron Working - the terrain suggested that iron would be easier to find than horses. After learning Iron Working I saw iron in the hills. France did not yet know Iron Working so I didn't trade it of course - it was possible to secure the iron first with one of my early settlers. I started research on The Wheel. After discovering The Wheel (1750BC) I saw the nearby horses in one of the intended hill town tiles. Of course that became a priority for an early settler. After The Wheel I researched Writing and then Map Making. After that I traded a bit, getting Horseback Riding in one of the deals. That was it for research. After that I did little research for quite a while. (None at all that I remember until Chivalry.)
After learning Map Making I built a galley and it quickly discovered Japan. I bought her maps to find out where Greece was. (Didn't trade my maps nor buy contact with Greece.) The galley sailed on to Greece and established contact there. Since I had seen no other galleys exploring yet, I held back the contact between France/Russia and Japan/Greece for some time. During this time I controlled the trading of maps, profiting a bit from each exchange. My galleys contined to explore, discovering more of the world and then selling this knowledge for gold and tech. I eventually sold the tribes contact with each other. Hadn't seen another galley, but did not want to lose the opportunity to profit by the exchange. My galleys discovered Egypt. It was fortunate they'd been isolated - they were the strongest tribe, but technically backward due to their isolation. For some time I eeked out technology to Egypt for the highest prices they could pay. And continued to profit from my advanced maps with all tribes. Eventually I also sold contact between Egypt and the other tribes.
During the time of exploration, about 250BC, my first army of 8 Swordsmen and 8 Horsemen (all veterans) attacked France. The war was brief and decisive, we took all French towns except a young one north of Russia. But it was an expensive war, costing a number of our units.
After this war I made the most important decision of the game: I did not attack Russia. Losses in battle were too high compared with our ability to produce new units. I redoubled the efforts to produce Horsemen and stockpiled them. I waited for other tribes to discover the prerequisite advances for Chivalry. During this time I built up the treasury as described above. (Zero research, exploring, trading.) When the required techs finally became available I had a reserve of about 2000 gold! I traded for the latest techs and set research on Chivalry at 100%. When we learned Chivalry I had about 30 Horsemen, and enough money to upgrade 21 of them to Knights.
Then began the Great Crusade!
The 21 Knights (followed by more as additional Horsemen could be upgraded, and the occasional new one as towns very slowly produced them) sliced through Russia. Only 5 Knights were lost in this invasion. We captured the Great Library, which quickly revealed three techs and made itself obsolete.
I granted Russia peace after driving her off the continent, leaving her with just some island towns. As before with France, I captured all towns instead of razing. I began the occupation of each town by starving the population to one, using some of them to build a temple when there were enough. I brought a settler with the Knights to create a new town for our Forbidden Palace. But the war created no Great Leader. (Paris continued on its very slow build of a Forbidden Palace as the backup plan, just in case. Fortunately that was never needed, that project was eventually abandoned.)
Our Knights remain strong and want to continue their crusade. Greece has the finest land in the world. If we do not attack soon I expect she will grow to become the strongest tribe. Now is the time to strike. Our culture overshadows Greece, we should be able to capture towns and keep them again. The Knights return to Washington and are ferried to Egypt. (7 Galleys were ready at this point.)
The first wave of 14 Knights slices through the Greek defenses. Regular Hoplites crumble before elite Knights. More Knights follow the vanguard. A few Knights remain to guard the home continent. These guards amuse themselves by capturing the remaining French towns - France is no more.
When Greece has been driven entirely off its homeland I give it peace for some island towns and tech. Losses during this crusade were very light, just a few Knights.
Near the end of the crusade against Greece a Great Leader emerged. (At last! It took nearly 40 wins by elite units before this, our first leader, appeared.) I settle Las Vegas in the center of the prime Greek lands and build Forbidden Palace there. (The gods suggested this town be named Buffalo. I could not bring myself to agree with that choice for the new cultural center of our world.
)
At this point I decided to play out the game. The date was already too advanced for me to prefer an early win bonus.
Japan had recently learned Chivalry. I decided to attack before she could produce many Samurai. The Knights regrouped and began this crusade. They encountered only two Samurai, but these were costly encounters - four Knights died subduing those two fierce fighters. Other losses were light (two Knights I think) and Japan was driven out of her homeland. I gave peace when the Japanese government fled to an island town. Our elites won 16 more battles but no new leader emerged.
I switched to Monarchy at this point. After rushing temples in some captured Japanese towns it was time to put the whip away, to allow Las Vegas to truly blossom.
I did not expect the Knights to carry their crusade even this far, but a strong core of elite units remains! Egypt's culture is as high as ours and she is growing rapidly in strength. I have slowed her research a bit over time by selling luxuries to her at high prices. Egypt does not have Saltpeter nor Horses. 13 Knights, almost all elite, continue the crusade to Egypt. This crusade has two objectives: 1) Weaken Egypt sufficiently to remove them as a long term threat. 2) Secure access to wines and ivory for our people. Two settlers travel with the Knights. A few more Knights will follow in a second wave.
The first wave of Knights destroys Sun Tzu's in Egypt and then destroys their three strongest cities. A great leader emerged from the first fight. The settlers establish two towns and the Knights retreat there to heal. We lost only two Knights in this assault! After healing, the Knights continue the crusade. They seem unstoppable, razing town after town with few losses. Soon the Egyptians, like the Russians, Greeks, and Japanese before them, are driven completely out of their homeland and take refuge on an island. The crusading Knights again exceeded my expectations. I quickly produced some settlers to claim the now empty land.
The first great leader from the crusade in Egypt returned to Las Vegas and built Copernicus's Observatory. Because we had already acquired
)) the Pyramids from Japan, this caused a Golden Age to begin. Soon after building Copernicus's a third great leader emerged in Egypt. He, our last leader, went home to build Adam Smith's Trading.
After driving Egypt out of its land I did some careful counting - did not want to trigger a Domination victory again! I decided to reorganize our holdings a bit, abandoning some bits of tundra in favor of the more fertile Egyptian lands. I decided to leave the remaining remnants of other tribes alone and to go for a cultural victory. The other tribes would be allowed to claim what they could in the remaining barren parts of the world.
The remainder of the game was uneventful. After the Golden Age we became a Democracy. A long period of peace, prosperity, and growth followed. Las Vegas became the cultural, intellectual, and economic center of the world. Russia and Egypt had taken refuge on the same island and this eventually caused them to have a brief but inconclusive war. They grew a bit, settling small outposts elsewhere. Japan never recovered, she remained a single size two town on an island. Greece recovered best from our Knight's tender ministrations, eventually growing to take most of the two large SE islands. Amusingly, in 2048 Greece demanded that we supply her rubber. When I refused (not that it mattered in 2048 but I would not give in on principle) she declared war. She even convinced Japan to join her. Greece attacked one of our towns with about 5 Cavalry, who died in their senseless assault on our Mechanized Infantry. In my final 2049 save, America is at war with Japan and Greece. Although America's military is small, it is powerful, advanced, and has an airport network for high mobility. Suppressing the feeble Greek attempt at war would be trivial if the game were continued.
In 2050 America won a cultural victory.
The French have four cities. I let them live. I may roll over them when I get Calvary.
It's now about 1650, and I was prepping for war against Russia when out of the blue Egypt attacks me. And this when they were already fighting Greece! Looks like Cleo was going through the "Crazy Catherine" syndrome of random attacks. Her loss - now the whole world is against Egypt, which has been frankly crushing everyone else in culture. I was seriously worried they would win a cultural victory before 1900. Well, looks like they won't be around that long now 
Thanks to Theory of Evolution, Wall Street, and finally a decent amount of territory, I am starting to pull away from the AI in tech. The fact that they keep wasting their money on pointless warmongering doesn't hurt either. I've got discoveries down to 5-6 turns at a profit, something unimaginable earlier. The key in this game, as in most Civ3 games, seems to be surviving until railroads; even with smallest territory I had the highest overall production of any civ. That and on this map you have to take out France early (this sounds like GOTM4...) If I had done that better (I lost a lot of battles I should have won against them), I might have gotten into the lead before the mid-industrial period.
Nice move using the money to steal some tech though 
