I did one last game to try a few new things out and fixing some mistakes.(sorry WC-Ente

I almost finished this game as you posted yours. )
It turned out to be quite a good game and i won in
1560AD - 222 turns(needed 7 hammers to finish one turn earlier. )
First i did go tradition for the 33% wonder production as erajah suggested. It was kinda messy though as i lacked SP points so i ended up getting the bonus quite late. I still have a hard time figuring out if its optimal, but in any case it doesnt cost you more than 3 turns max, so its not a big loss(assuming you get about 350-400 SP points per turn during the endgame.
My order was:
Unlocking Tradition -> Unlocking Patronage -> Aesthetics -> Philanthropy -> Scholaticism -> Aristocracy -> Cultural diplomacy -> Unlocking the freedom tree -> Constitution.
If i took Aristocracy first it would result in me having to wait to get my maritime CS policies, and that just didnt seem worthwhile. Therefore i got it as late as i did.
Unlocking the tradition tree first was not optimal either, but i needed that extra food badly in my capital, to remain stagnent.
I managed to get 2 puppet cities(london and Istanbul in 33 or so turns(even got 2 extra workers also

)
I beelined to Acoustics like last game
Pottery - Calendar - mining - writing - masonry - philosophy - Theology - Education(GL) - Acoustics(GS)
But this game i reached it in 62 turns!!(This must be quite close to what is even theoretically possible atm)
My goal for my capitol, was to get to size 4. Then put 2 people into the library(which i bought), while the others focused on wonders(my city was stagnant at this point)
When i had the CS SPs needed i allied with 2 maritime CS for a +10 food bonus in my capitol. From there on i spent my gold on allying cultured CSs.
Then i got horseback riding, and beelined to Astronomy
Animal husbandry - The wheel - Horseback riding - sailing - optics - compass - astronomy
I made sure i had 3-4 horsemen to find and invade the other continent(s) as soon as astronomy was up.(only one AI remained on my continent(america)
Basically i conquered the first city on the other continent around turn 110.
After this i finally went for Civil service.(mostly cause i didnt work many farmed river tiles.
I think i did make a mistake here as i probably should have taken trapping much earlier so i could start making trading posts in my puppet cities.(instead of farms)
Especially my gold income was a problem during this stage, to the point where i could'nt just buy all my buildings and focus on wonders only.(had to build monument, temple and one other myself)
Beelined to biology:
Trapping - Civil Service - Navigation - Archaeology - Scientific Theory(oxford uni) - Biology(GS)
Biology i got much earlier this game for the extra culture gain.
Then beelining to Printing press.
Cause i spent a extra GS early i had to invent Steam Power myself this time.
Electricity was invented using another GS and Telegraph using the GS from The Porcelain Tower.
Also this game i was much more aggressive and ended up with more puppets(19 in the end)
I even had to be careful not to take the last AI capital

)
Its the first game where i have managed to basically conquer the whole world, with my small army.
After Christo was done i still had to wait some 15 turns to finish the remaining SPs.
To save some turns in the endgame i focused solely on growing my capital after christo was finished to get as many hammers as possible once i had to start the Utopia project.
Also as soon as i unlocked the last policy i annexed as many cities as i could without going below 0 happiness.(annexed the oldest ones)
These cities focused solely on research(building research also)
This way i could get to plastics and Ecology faster, and buy a hydro plant in my capital + a solar plant. That saved me 3 or 4 turns.
Electricity(GS) - Telegraph(GS) - Radio - Refrigeration - Plastics - Penicilin(GS) - Ecology - Globalization