To date, I haven't really worried about Great People after the first 3 Great Priest pops. But now, I need artists to help time the cultural victory correctly. I hunt through my cities and find one with lots of food and send nearly all of my workers over there to farm it all - even dyes. I actually had my workers re-setting some cities during the game. My cultural cities were reset to commerce ... it was hard destroying the workshops on my Ironworks city (ex Khan capital) but it had lots of culture and was thus set for legendary status. After I had almost finished all the teching, various cities got workshoped to build the parts. Then, finally, after the ship was finished (it sat for about 15 turns before launch) every non legendary city was farmed and the culture slider was turned up a few notches so that I could grow my cities (bigger cities means a bigger score). The other option for a higher score was more tech but I thought that the population increase would yield more points. I did leave some cities with heavy hammers so knock out some wonders.
In 1951 (turn 371), my capital (Istanbul) went legendary. In 1955 (turn 375), I burnt two of my Great Artists and Karakorum went legendary. In 1956 (turn 376) the final war against Spain was started and the Ship was launched. In 1965 (turn 385), the game was in this position ... and after burning my 3 other Great Artists, killing Isabella and settling about 6 or 7 cities ...
Oh - and I did win a UN vote on that turn too ...
My final Firaxis score is 33,443 and my multiplier is 25 (Culture, Domination, UN, Conquest and Space) for a total score of 839,075.