OK - space race victory in - ummm - 2008. Final score: 6919. I decided from the start that I was going for the space race - I know that runs right against the Kublai Khan's traits but I felt like it
That meant I was going for a strategy of high science throughout, and only limited warfare - enough to make sure I was slightly bigger and better than any one other civ.
In the event I won, but IMO this one of the my most pathetic Civ attempts I've ever played - due to a mixture I think of me being careless because of playing at Noble level (I normally play at Monarch) and me experimenting with some new strategies, some of which it turned out didn't work too well. I got a 2008 victory, but I'm sure on noble I should've won a space race a lot earlier than 2000ish. And I wasn't that far ahead of Mansa Musa either, who started spaceship building at the same time as me.
Though having said all that, after winning I read through some of the other write-ups and realize that the map probably was harder than typical noble: Financial opponents, long distance from other civs, and lack of resources, especially happiness resources, nearby.
Final situation as figure:
Game Summary:
In keeping with the plan of high science, I beelined for pottery first to start getting cottages. Then planned to find out where the horses/copper/iron are, then try to found Confucianism, picking up the hanging gardens and great library on the way (and I did pull those off).
Because of the low difficulty level I wasn't expecting a rapid land-grab, so I experimented with not building any settlers initially: Instead I waited until Karakorum was close to its happiness limit. The advantage was that by then I was producing a lot of gold - so my research got off to an excellent start, and building a settler was very quick. Not only that but it meant I knew where the horses, iron and copper were before I founded my second city, so I could make very intelligent city placement choices. Doing it that way would never have worked on a high level or with other civs close by but was doable here. Not sure I'd do it again though - it really slowed down my growth. On balance I think it hurt more than helped in the long run.
I slowly populated the starting land area. I lost control of the pinch point - there was a barb city there which Bismark took just before I could get it. Since by then I was spreading Confucianism through German lands and he was becoming my friend, I decided not to take it back, but to keep him as a friend, and keep open borders so I could still use the pinch point, and conquer someone else beyond. In the end I took out the Japanese - one war with my cavalry that reduced him to 3 cities, then a later war in the 19th/20th century to eradicate him.
The Good Things
The Victory
The plus side is this made for a very exciting finish, with me and Mansa starting spaceship production about the same time - so I was building spaceship parts at the same time as using my spies to keep an eye that Mansa really was falling behind (he was - he just didn't have the production-geared cities that I had to build quickly), and I was simultaneously building enough military to keep open the option of declaring war on him, if it looked like there was any serious danger he'd win.
Conquering Japan
I have to say that conquering Japan worked well. The final map has to be a text-book example of using the forbidden palace: My civ divided into two big regions, both not too hard to defend, and with the 2nd one 'serviced' by the forbidden palace. So you have a big civ but economically quite viable:
Cavalry
Another thing that went well was a strategy I'm starting to use quite a bit: Beeline for liberalism, pick up nationalism as your free tech, use that to get cavalry long before anyone else, and then do your big round of conquering with the cavalry. It worked a charm - Japan melted before my cavalry/catapult combination. An odd side-effect was not only that I never built a single keshik, but because I was mostly using mounted units, I pretty much completely threw away the advantage from the Kublai's aggressive trait. But it worked. Once I had Japan I focused on building my economy, keeping enough defence to defend myself (against the Chinese and Greeks, who never liked me and declared war a few times, though they were too far away to actually do much).
The medic scout
You know the strategy of using explorers as medics - well I very successfully used a nice twist. During early exploring, one of my two scouts managed to get promoted enough that I could give him Medic 1. And - you guessed it, he travelled with my cavalry into battle, always well guarded, but always right where the most intensive battles were being fought. He hugely speeded up the war. And he's the first ever scout I've had to still be alive at the end of the game, in the 21st century. I think he deserves a medal. Here's a picture of him basking on the coast in his post-spaceship retirement.
Culture
I'm really starting to appreciate the power of culture, not only with a culture bomb, but with slow building up - getting every religion you can into a city on a border and building monasteries and academies like there's no tomorrow. It's slow but works wonders. Look at Nagasaki a while after I captured it from Tokugawa: It's very hemmed in by the established city of Dortmund
And now years later.
I did actually use a great artist in Nagasaki, which I think is why Dortmund eventually flipped to me, but I'd already captured most of the land between Dortmund and Nagasaki from culture buildings alone before the great artist was born. Matsuyama (captured by Germans from Tokugawa) stayed German to the end, but look in that last screenshot how many units Bismark had to keep in it to stop it flipping (The list of units is the ones in Matsuyama), and look at its size: Confined by high-culture cities all around to desert - despite reaching an 80% culture defence bonus, it ended up still at size 1.
A lesson in how to keep friendly civs under control without going to war. Can't build your whole strategy around it but very useful occasionally!
Amphibious Promotion
Oh, and one other thing I quite enjoyed: This game saw my first ever serious use of the amphibious promotion. It never seemed appropriate before but this map shows why I used it now: Japan's last city, Shimonoseki.
China is furious/annoyed with me so I've no chance of getting open borders with them. With that mountain there, there's no way to take Shimonoseki without either declaring war on China or attacking direct from the sea. Literally, after I'd taken every other Japanese city, I was building a transport and hunting through all my units to try and find some artillery and riflemen that I could give a quick amphibious promotion to before sending them off to the island. It worked! (I didn't even want the city, I just wanted Tokugawa completely vanquished to quell my restless Japanese 'we long to join our motherland' citizens)
What went wrong? Well…
Chopping
This was my first serious game with the 1.61 patch I wasn't too sure how best to adapt to the new lower forest chop yields - I ended up not doing any chopping initially - thought I'd wait for mathematics, then when I had mathematics, there wasn't anything I needed urgently so I still didn't chop. My first forest got chopped in order to help build the Taj Mahal! Not chopping did have benefits - it meant when I was ready to build the spaceship, it was relatively easy to select several cities as high-production ones and hence get the ship built quite quickly, along with the Space Elevator and the Internet. But it really hurt my early expansion. With hindsight I probably should've chopped a bit in the early game. (If nothing else, chopping would've stopped me losing the pyramids by 2 turns).
Sheer carelessness/laziness
Things like leaving workers on long go-to instructions in wartime (they walked right into the enemy), and on one occasion, giving an unescorted settler a 10-ish-square go-to instruction. Turned out there was a barb city on the spot I told him to go to. He just walked straight into the city and - umm - died inside it. Oh and forgetting to regularly check the relations between the AI civs (hence not noticing that the Greeks I was at war with had got an open border agreement with the Germans and hence would be able to turn up out of the blue along the Mongol-German border). Oooh that gave me a scare as well as a razed city! (It was also the main reason why I abandoned my first Japanese war when Japan still had 3 cities left).
Cottage-spamming
Not tried cottage-spamming from the beginning much before, and thought I'd try it this time. I think I overdid it - really helped with science early on, but the lack of farms meant my cities grew too slowly and that slowed me down in the mid game.
No Micromanagement
I really got too lazy with that, just letting cities manage themselves and not checking up on them for long periods. I think that hurt my game almost more than anything else. For example, at times I think I must've had cities for hundreds of years failing to grow because I hadn't noticed they needed a few more farms or I'd left them on emphasize production when there was nothing urgent to produce.
Religious Coordination
Normally I complain about wonders giving me too many great prophets. This time I founded Confucianism and Christianity but didn't build any of the great-prophet-generating wonders. The result was two religions spreading nicely but I couldn't benefit financially coz I couldn't build either of the shrines! I initially didn't have any cities with enough pop surplus to comfortably put priests to work in, picked one anyway, but then the two priests in it couldn't keep up with the (non-prophet) GPPs from the city that did have most of my wonders in. Finally got the Confucian shrine-thingy sometime in the 1000AD's I think, and - wait for it - built the Church of the Nativity in - sometime in the 1950s if I recall correctly.
Diplomacy
Must remember to use the trick of having AI's declare war on each other
appropriately. My big successful war was with Tokugawa. Obedient to best practice, I bribed Bismarck to join in so I could get by with fewer troops. Why did I do that? I had cavalry, Tokugawa had horse archers (Well at the end I think he built one knight before I removed his supply of horses). I pretty much sliced through him, scarcely losing a single unit, and with only one city supplying all my military needs too! I basically ran a peace-time economy throughout the war! I soon had to bribe Bismarck again to make peace with Tokugawa (at quite a heavy price too, pretty much halved my tech lead over him), just so Bismarck wouldn't capture any cities and so deprive me of the certainty of taking them.
Summary
All in all a good game. Although I wasn't happy with how I played, it meant I could fit it in over a weekend. I enjoyed it, and the map was a slightly unusual challenge. Thanks Ainwood again! (and AlanH)
Thanks a lot. 
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