Continuing from 1 AD...
MM had lost Djenne to barbs and hadn't moved to take it back. My axemen did the job in 50 AD, and to my pleasant surprise I discovered that this was the Jewish holy city. So now I had three native religions. I'd add Taoism to that list in 400. (Buddhism would later spread to one of my cities, but would play no role in my victory strategy.)
I used a GP for the Kashi Vishwanath, built the Mausoleum, then used a GP for one golden age and built the Taj Mahal for second, long golden age.
I ended up researching up to Democracy, when I finally switched to 100% culture in 1220, running Universal Suffrage, Free Speech, and Caste System to generate as many GA as possible. Once I had eight of them, (not counting the starting two that I had culture-bombed in the BC), I culture-bombed them all to win a Cultural Victory in 1695. Well behind Tobiyogi's pace.
So, what mistakes did I make? One was a simple one; I traded for Economics in 1250, then neglected to switch to Free Market until one of the AI urged me to do so in 1615.
More fundamentally, I think I concentrated too much on the tech path that gave me the Liberalism bonus in 1030, and only then researched Music in 1040. I needed to start building my cathedrals much earlier. And I completely forgot to build the National Epic. Temporarily switching from Caste System back to Slavery to whip those Cathedrals might have been worthwhile, too.
Incidentally, MM built the AP (Christian) in 1040. He had Christianity spread to all of the AI at that point, but he never made an effort to spread the faith to me. It was nice not having to worry about my victory being stolen away!
Oh, well. Thanks for the game!