So big picture items (sorry for the long list but these are just my pre-game thoughts):
1. We should go for UN, unless somebody has a very convincing reason why culture will be faster/safer. The fastest way to the UN (assuming we pick up two vassals to vote for us) will be a straight bulb down the radio line capped by liberalism for radio (mass media is cheaper), although I'll have to do test maps to see how reliable that is on emperor. I think it's reasonably doable since we're philosophical.
I like this statement,

Plastic Ducks Notes
Settled on PH, as well. Their settling pattern was very different from ours. Bombay went 2S of stone instead, and they settled Vija NWW of stone (!) before 2000 BC - this was their GLH city. Pata (Two Fish equivalent) went SW of pig, giving up one of the fish (?!) They lost the Oasis site to Zara and didn't go for Ivory. Instead they planted the two gold cities next to Saladin relatively early.
Bombay was settled that way since it could save a monument and can use the copper right away, Bombay pumped 4 settlers including the one for Vij and some workers.
For the same reason, in that position, Pat can work on 3 resources without border pop, which is much more efficient for unit pumping at that stage an extra fish only adds 2 specialists and our main GP farm is capital.
The 2 fish and ivory site was gone before we saw it, whether to claim it depended on the random factor/ AI's behavior.
Oracle (COL) was built in 1975 BC in Delhi, and they got a touch lucky with their first two GS popping at 70-80% odds. Delhi built Pyramids next, then ToA, while Vija got GLH. They went for Lit before Philo/Paper/Educ, and built TGL in the BC's. Seemed to be slightly ahead of us in research circa 1 AD, our early Oxford and direct beeline pushed ahead in the 1-500 AD period, but they crushed us in the end, riding the wonders, extra GP's and continuous golden age.
Both GS was at over 80% odd, so it's almost for sure we can get 1 for academy, Gpriest is almost as good as GS in early stage.
All our micros in early stage is to grab GLH, I was the only one who was satisfied with the natural completion date of > 95% successful odd.Other members wanted to whip Vij to get it 2 turns earlier. Therefore, a plan of oracle to get CS sling will be denied in our team without doubt since they want critical wonders to be as safe as possible.
We could have OU on line as early as before 100AD, which is a close date as yours. However, we decided to go to war as early as possible, which not only sacrificed our research, but also GPP since we also gave up Part.
Not sure the extra expansion mattered so much. The gpp RNG is substantial, as they popped everything they needed without really trying very hard, whereas we over-dedicated at every juncture and failed (not only the GE obsession - remember also the 5 pages of discussion about the academy GS and all the mess around the second GM). The Delhi gems make a difference, too. All in all, I think gems, better luck and taking out Zara might collectively amount to a closer margin (more like 4-5t instead of 10-11t), but their base strategy (primarily Delhi usage and wonder-spam) seems to be superior.
We indeed had pretty good luck on GP type, but some of them does not matter such as if there's a Gpriest in the 1st 2 GPs, or another Gpriest in the middle, which could be used to launch a GA and we could save the GArtist to bulb MM.
Our luck on the gem is not that good as you imagined, kossin get it ~600BC, however he also get a demand from Toku, which cost us ~15 turns to adopted Hindu to fix it while our major cities were all Confu, lose quite a lot trade route income and whipping hammers from OR bonus.
I guess if the research phase was shorter - we'd win, and that if it was longer - we'd get absolutely massacred. The break-even point is somewhere around Physics/Electricity?
Remember that we also researched Nat and built Taj, therefore if the research phase was shorter, we could skip Nat and go for SM directly. Our research was greatly weakened during 1AD~500AD since we were whipping many cities to hell for the war.
Last, I would not say which strategy is better since both teams did a very good job to secure the win ~1000AD. but the way of getting vote by force is safer and more flexible in bad diplomatic situation