I finally got my first sub-300 tech victory (Korea, Emperor, turn 279). I wanted to write one more post to supplement the other advice in this thread for anyone else who is having trouble improving their tech times.
First, about the benchmarks: forget them. I'm sure if you want to win at turn 200 then every move you make must be perfectly optimized, but if you just want a solid tech win then it's much more important to focus on the fundamentals - happiness, money, defense - than stressing out over whether you're going to hit Scientific Theory by turn 160. In my game I got NC at 81 with 3 cities, Education at 115 with 4 cities, Scientific Theory at 174, and Plastics around 215 (I lost the save).
Second, religion is insanely helpful - it's probably the the single factor that made the biggest difference for me between turn 325 tech victories and a turn 279 tech victory. Include a shrine early in your build order - you can go scout-scout-shrine if you get a cultural ruin - and select the pantheon which will give you the most faith in the short run. You want to get tithe at all costs, and either Pagodas if your pantheon gives you lots of faith or religious center otherwise. The reason is there is a certain point in the mid-game - starting a little before Scientific Theory for me - when you start to face severe happiness and financial pressure. The financial pressure comes from the fact that the AI eventually stops buying your horses, a nearby civ is massing at your borders and you need to bribe them into war with someone else, and you want to save up for the next science building. The happiness pressure comes from the fact that 3 of your 4 cities are on rivers and civil service is really starting to kick in. It just happens that tithe and pagodas / religious center provides you with just enough money and happiness to get you through this low point, and the rest of the game is smooth sailing (with tithe paying quite handsomely in the endgame).
Third, don't freak out about culture and faith. You only need enough faith to hit 1000 before you research satellites, and this takes less than 100 turns if you build 4 shrines and temples. Everything else you get from your pantheon or city states is icing on the cake. As for culture, it's OK if you aren't burning through social policies in the mid-game, though you probably want secularism ASAP (especially if you're Korea). The reason is that you can catch up in the mid-late game if you plan ahead. Build and staff the writer's guild as early as you can (probably in your capital) and save all of the great writers you generate. Make world's fair your second proposal, and make sure you win it (this should be easy, at least on emperor). Before you win it use some combination of money and spies to make sure you're allies with as many cultural city-states as possible, and start a golden age with a great artist saved from your artist's guild as soon as world's fair reward kicks in. Wait 8 turns and pop all of your great writers. In my game I got over 6000 culture from the pops; combined with the free social policy and extra culture per turn from the world's fair/golden age, I think this was good for 7 social policies within 10 turns (and I managed to time it so that one of them was the rationalism finisher, used on satellites).
Fourth, you don't have to spend much money on city states. All of the good players say they don't spend any money on them, and I never understood how they got by. I probably still don't entirely understand, but I think part of the answer is the effective use of spies. Every time you get a new spy, immediately put him in your capital and let him kill enemy spies; he should hit level 3 quite quickly. Then steal the AI's city state alliances with coups, rigging an election first if the coup probability is under 75%. This process is free, it only takes a few turns, and the diplomatic hit isn't as big as if you steal the alliance with money. So by and large you should save your money for buying science buildings and upgrading your military, though it's probably OK to throw a little money at a mercantile or cultural city-state in the early mid-game if you're struggling.
That's all for now. On to immortal...
. Sometimes you just have to play it through to get it 
