I've had a quick first run at this, with Gandhi/Inland Sea. I self-built
eek
21 cities IIRC and finished in 1620 (t152). I have another game in progress which should finish before then, as I overprioritized ReX in that one, and was a bit sloppy at the end.
The game seems to be divided into three stages:
1. Founding initial cities, clearing basic techs, and getting into bureaucracy.
2. Expanding into a large empire, building Oxford and researching to Assembly Line, Communism and Biology. (or similar Industrial Era techs)
3. Researching to the end of the game, and building some spaceship parts.
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Looking at the game, we have two problems to solve.
a) We need a large amount of total research.
b) We can't research more than one tech per turn. (With possible exceptions for early trades, lightbulbs and Oracle/Liberalism).
(b) is particularly relevant to Quick speed, since technologies are relatively cheap, and with your high bpt, you might be able to research, e.g. 5 techs in 3 turns, but for this.
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For stage 3, techs take 1 turn each, or thereabouts, so the key to improvement is getting there faster, as opposed to focusing on endgame research.
How can one do that? You still need to build or capture many cities, and build a hundred or more workers, so while there is room for efficiency here, there isn't all that much you can do to reduce the hammer cost of these.
So, the focus should instead be on the research requirement to get to stage 3. In the latter parts of stage 2, empire-wide research is not quite high enough to maintain 1 tech per turn; I'd estimate you can save 5-10 turns or more here, although I'm not sure what the best way to change it is. Maybe it's a second dedicated cottage city, although it doesn't sound like the best answer. Maybe having an Industrious opponent build the Pyramids for you would help, too. A third option would be using the Financial trait (possibly this is the best of the three).