I think everyone needs to look at the broken percentages for domination. They are absurdly low this game. We *must* get multiple people to vote for us. There is no way around it.
If this is true, then the winner of this event will be determined by luck rather than skill. Randomly distributed religious diplo bonuses will dominate the early opportunities for improving relationships. This is especially true with aggressive AIs.
In that case, we're already out of the running for any kind of fastest finish because we didn't choose a clear diplomatic plan from the start. Of course, the reason we didn't choose one is because no obvious choice presented itself to us. Perhaps the majority of the other teams settled their capital somewhere other than where we did and therefore somebody like Gandhi founded Hinduism or something and boom: all the nearby civs are buddy-buddy with each other. Easy diplo victory.
I think we can (and in fact must) find a way to win a diplo victory without many (or even any) friends. It may require some tricky timing of our last few city captures so that they are in revolt when the diplo victory vote is taken, but that's fine.
What kind of relations do we need to get other civs to vote for us instead of abstaining from the victory vote? Something like +11 or +12, right? Looking at Bugsy's list, I see possibilities for +4 shared religion (with civs who care about that), +4 fair trades, +4 favorite civics and other bonuses to counter "worst enemy" trading deals. We might be able to do that with a couple of civs, but it depends a lot on the luck of which religions go to which civs and whether their favorite civics are mutually compatible or not. It also requires that there be another civ out there who is big enough to be our diplo vote contender, and we won't be getting those votes.
What does it really mean that we need to stay below 51% land and have 62% population? It means roughly that our average city has to have 20% higher population than the average AI city. By concentrating on taking high-food cities, we should easily be able to manage that. In addition, there will likely be some backward civs near the end of the game whose capitals we can quickly take with several boatloads of troops.
In a crowded map like this, every possible city site will be settled by one AI or another. This means that on average, each civ will have cities ranging from a pretty good capital to some really poor no-food-bonus sites. We can be somewhat selective and concentrate on taking the food-rich cities. For example, with Greece, we don't even really need Sparta, it's Athens that we want with all that glorious seafood.
As for a conquest plan, it's generally best to take on the leaders. This is for at least two reasons. First, the leaders tend to climb the tech tree faster--and with so much tech trading here, any increase in the AI tech rate is bad--so we want to stop their progress. Second, since all the AIs follow roughly the same strategy, those with the highest score have the best land, and we're looking for the best land.
What does this mean for us?
I think it means that we should conquer several Roman cities now. All the good ones that we can see.
Then, I think we should take Athens and Sparta. If at a later date we need to ditch a city to lower our land holdings, we can gift Sparta back to Greece. Then, I think we need to take a bite out of Mao. We should take all or almost all Chinese cities with a good surplus. We might also need to take another couple of cities to reduce cultural pressure.
Then, I think we need to take out Hatty. Mainly because her good score implies that she has good land. With luck, she has a city somewhere off of here main island. That would mean that we could take all the cities on her main island. If we're getting too much land before we're able to run the diplo vote, we can gift her then-defenseless cities back to her. We can always re-declare war and unload troops directly into the cities from a boat, taking them (and their precious votes) instantly.
With a high power rating, no other civ will attack us, at least not in any meaningful way.
Note: nearly crossposted with Tatran. I completely agree about Mao. A pleased Mao is about as safe as an annoyed Mao. Better to have a conquered Mao.