Game date: 1565AD
Turns played: 223
Base score: 3094
Final score: 7031
Time played: 19:07:00
Where to start.. well, I applied the same tactics I have found to be most effective when playing CVs on immortal/deity (actually on immortal its not necessary since you can grab tech lead so early). This seems to be about the same approach glory7 chose. I think it should be superior to a peaceful CV here because the dirt (cap) is nothing special (hill, river, no mountain, no desert, no mining luxes.
First 100 turns should be outlined in opening actions. Opened 3-city NC and placed a fourth city right after. Wanted to place it on the isthmus to the right, but Pacal took it (bad scouting/guarding) so I had to settle for another mountain city in between the Sinai one and the stone/marble one. Worked out quite well, might actually be better than the coastal spot just because of how strong observatories are. An early DoW (T70) by Assyria was thwarted by the great strategic position of my Sinai city - it was only accessible through two tiles so I held quite easily with nothing against a decently sized army. DoWed Pacal again to steal another worker around that time and delay his oracle. Forgot about it (..) and he built it anyways. Education t105.
Policies were full tradition (with culture ruin), then Patronage - Consulates - Scholasticism. I had so many early CS allies that I could easily afford going Scholasticism without delaying Ratio, because I wanted to enter Ren with Astronomy anyways. AIs except for Assyria were very friendly early on, so I could gather enough gold for a lot of unis and observatories. SPT soon soared and I was quite indecisive at first, if the path to pursue would be peaceful or world domination (the latter I was already used to on this difficulty). Hence I chose a tech path towards Printing Press skipping Acoustics and if I recall correctly I even founded it. Since my tech lead was already ridiculous (3 observatories and huge cap) I was thinking peaceful CV, but someone built Sistine before I could have grabbed it even with Acoustics teched earlier. After seeing cultural output of India and Maya, my choice was warring.
Beelined dynamite. Already had some Xbows (thanks to Assyria) and declared on Pacal, mostly to steal two more workers and also to take Uxmal which was my preferred 4th city spot. Unfortunately I had delayed upgrading them due to my indecisiveness before Sistine so I was not able to take it down. Fortunately Assyria declared again and I could put them to some use at least. Meanwhile ignored tourism completely. Great Writers (quite obviously) went to speeding up my policies so I had Free Thought very early.
I hit Dynamite quite confidently around t150, using one GS and 4-5 RAs. I had slacked on unit production though (whoring culture buildings with the aes -50% production). Immediately switched tech to Science focus. Artys took down Assyria quickly and proceeded to Spain. Got second army to march east but as it turns out, quite late. Should have switched all cities to unit production to kill them off quicklier. They eventually captured Pacals main cities and went for India (which I eventually completely destroyed) and Brazil. Assyria, Spain and India were removed from the game. Pacal had 2-3 cities left but wasn't doing so good on culture (~6k). Unfortunately, India and Brazil had placed colonies all over the map. It was quite tedious taking them out. I sold my useless puppets to Theodora and monitored her cultural output to make sure she wouldn't pose a threat. She eventually built Louvre but I had forgotten about it anyways (no time to open exploration).
T215 Internet was researched. Meanwhile there was only Brazil and India's last city that posed a cultural threat. Since about 10-20 turns before I had been wondering if I needed NVC. I did not have enough faith for 2GM + GE since I had already used one GE on Eiffel Tower and lacked faith. I was also early on GM production since I had stupidly built musicians guild too early (and just the natural GPP of the guild was enough..). So one popped quite early for a measly 1730 tourism. But my biggest mistake was forgetting to reassign the specialists - so at t210, I realized Warsaw wasn't working musician specialists...´
I could have gotten Internet some 5 turns faster too, but I have the bad habit of conquering cities in the same turn as bulbing and thus increasing my tech costs..
The major issue was not conquering fast enough to the east. I had underestimated how long it would take to push through Pacal (ugly terrain) and sometimes there were unnecessary happiness constraints. Eventually Brazil made a paranoia city (I checked the cities tab in peace negotiations and there was one I could not see even though I had explored the landmass thoroughly) that kept my workers/(captured) archaelogists busy scouting the sea. Finally I found it - it was precisely 5 tiles from the shore and only one land tile. So my promoted artys could not hit it and I had no nearby coastal city to capture it. I frantically tried to get GW bombers there but again, since the slow capturing, Brazils major cities were still in resistance so I could not rushbuy there (and GW bombers take ages to get across maps..). Also it meant I wasn't able to use their wonders properly, as well as having rather low tourism output - Assyria and Spain both provided little, India had moved all of it to his dying colonies and Brazil did not manage to recapture his capital for three (!) consecutive turns in a promising position.
So I had only ~390 tourism with Internet. I got a few GWs and theming boni from India as well as ending resistance in wonder cities a turn later, which boosted it up to 470. I couldn't kill Brazil fast enough, but also hesitated to buy another GM with faith. Instead I waited for the first pop to see (really dont know why I did that) what I could have calculated instead. Hence I could have won about 10 turns earlier - 3 3900 strength GMs (2 faith, 1 natural) would have done the trick. With proper warring and GM abuse (Broadway!) it should be possible to win around t200. Perhaps a hybrid between some warring (to get 2-3 more cities for tech) and otherwise peaceful (wonderheavy) approach could be fastest.
Pretty incoherent but my play was too

When warring, my turn times just increase disproportionally. After t120 I played sessions of 10-15 turns which amounted to more than two hours each.
One note for admins: I had installed the beta for MP, but forgot to remove it, then loaded t170 regular save. Clicked next turn and saw my influence drop with all friendly CS (in the beta pledge to protect only grants you 5 influence so they all dropped neutral). Exited game and removed beta. Loaded t170 save again, replayed the turn as best as I could (just tedious clicking, no major decisions) and continued. Hope this is no problem..