After hitting next turn, the year ticked over to 1758 and I won my Conquest Victory:
In a meaningless but nice coincidence, my score just crossed the 4000 mark on this turn. An appropriate symbol of victory. 
As far as scoring purposes go, here is my largest city at the time that the game ended:
Big City is up to size 29 and still growing. Unfortunately, I simply conquered the world too quickly for it to reach its maximum size. I wish that I had had more time to play around with this and build a truly huge city; I had several different ideas about how to get the city to gigantic proportions. My Medicine research that you may have seen in the previous screenshots had two purposes: first of all, it would let me build a hospital here in Big City (+3) health, but more importantly I planned to revolt to Environmentalism to take advantage of the huge health boost that comes with that civic (another +6 health). Along with a supermarket later on at Refrigeration tech (another +4 health), that would give me 36 health in this city. If I were to research up to Genetics, I could even get Big City to 39 health. With the two Great Merchants I already had in the city, I certainly could have reached size 37, and possibly further than that with more Great Merchants. But I killed the rest of the world too quickly for that, and didn't get far enough down the tech tree to put all these ideas into practice. You know what they say about the best-laid plans...
There is no way on earth that five people won't have a city to at least size 30. I'd be extremely disappointed in our community if I got any points at all in this category. The winner should be able to get a city close to size 40; with Caste System + Pacifism + merchant specialists, someone should be able to produce a LOT of Great Merchants. I'll be curious to see just how far down that path someone manages to get.
Here are some shots from the replay:
The most interesting thing to observe early on was that Louis' expansion was REALLY fast in the early going. I did remember being concerned about that early on. He was not only faster than I was (by quite a bit), but outdid the other AIs as well. In fact, Louis had his fourth city out only slightly after FDR's third city! Wow. He was really soaring along, so I was extremely glad that I was able to hamstring him early on. I actually declared war when I had one city and Louis had three - not sure what that says about me, but it can't be good. 
As far as the geography goes, I'm still faintly disgusted by the continents that the map produced. These particular settings almost never put two civs together in my test maps, and here we ended up with two big continents which each contained a pair of civs! This is an archipelago map, not a continents one! Oh well.
By 5AD, everyone has spread out quite a bit. The most remarkable thing about these particular years was the slew of wonders that Hatty was throwing out there; she had stone at her second city and just started going crazy with them. Stonehenge in 1090BC, Pyramids in 700BC (!) and Oracle in 535BC. Certainly the Oracle was there for the taking in this game, but the others went quite early. FDR grabbed the Colossus in 80AD, so that fell quite early too. And since Louis is one of the biggest wonder hogs in the game, I expect that he'll get into the action as well in games where the player doesn't declare war on him. For that matter, Louis DID have stone near his start too, and a marble within range in the north (alough the player could get to that one with an early push). I rather strongly suspect that I'm going to be reading about a number of players who tried for certain wonders and were beaten to them. Given that there was no stone or marble near the player's start, cultural victory may prove to be an interesting journey! 
The biggest thing that stood out for me by 1000AD was that Louis had failed to make much progress at all since 5AD. While everyone else had continued to expand and grow, he only managed to add two cities during the intervening years. In fact, I largely managed to contain him to his starting peninsula; only the new colony of Avignon has gotten past my borders. I could be wrong, but I think that I was able to get several cities in the north that clearly would have been founded by Louis in the normal course of things. I estimate that my pillaging campaign in the BC years slowed him down by about 50 turns, making my later conquest of him massively easier. The one drawback is that it did slow down my teching by having Louis as an enemy instead of a trading partner, but that was par for the course.
By 1500, I had completed the conquest of France and gained control of virtually the whole starting continent. Hatty and FDR have finished settling their own continent, and are preparing to expand overseas, awaiting only Astronomy tech to get started. You can see even more wonder completion messages for Hatty here (geez, she really wanted them in this game!)
Conquest halfway complete, I've eliminated Egypt from the mainland and am now hunting down Hatty's last island territories. Fortunately, aside from one little city planted on the island east of my continent, FDR had not really expanded overseas. That helped make things a little bit easier.
Conquest complete. Lots of nice red text over there on the right. From start to finish, the conquest lasted from 1682 to 1758, which comes out to be exactly 30 turns. It took 13 turns to eliminate Egypt's mainland cities, and 17 turns to defeat FDR. Given that FDR had rifles and Hatty did not, I think that means I was pretty equally efficient in attacking both.
And the statistics screen. Aside from seeing the number of units that I killed, and the many cities that I built and razed, the truly amazing thing is the number of rifles that I built. I currently have 29 rifles, and I've lost some 23 of them in the fighting (high casualties!), so that means I produced almost 50 total. Yet look at the number of rifles I actually built. ZERO! I didn't build a single rifle! 
Apparently I drafted every single one, which I find to be pretty hilarious. Also note that I had 18 frigates and 26 galleons, which is probably more naval units than I've ever built before. I needed all those galleons because unlike a normal campaign, I wasn't dropping off soldiers and then heading back to ferry more troops. No, the galleons sailed over to the other continent and stayed there to keep carrying the rifles from city to city! Therefore, every three conscripts needed a new galleon to send them over to the warzone, and so I ended up with a lot of ships. Not pictured are the many cannon I built and lost in suicide attacks to weaken defenders. They were also a critical part of the conquest.
Scoring
Conquest Victory: 1758AD
Population in 5AD: 866,000
Population in 1502AD: 17,326,000
Large City: Size 29
Did not reach Modern Age
So as far as winning a Conquest victory, this is clearly "pretty fast", but is it the fastest? I have no idea, but I think there's plenty of room for someone to do this faster, perhaps significantly so. I did this about as fast as possible ON THE TECH TREE, and I don't think you could conquer the AIs any sooner than frigates/galleons and rifles/cannon. However, I wasn't exactly rushing through the tech tree in this game, as evidenced by taking Liberalism in 1580AD. I think it would have been very possible to get through the tree faster, reach the same units I did at an earlier date, and then reprise my conquest in the 1600s, or even earlier. I'd be enormously pleased to have the fastest conquest victory, but I really don't think there's anything stopping someone else from reaching Astronomy in, say, 1300AD and then carrying out an earlier conquest. Myabe I'm being too hard on myself, but our community has some very, very good players, and I've learned not to underestimate them. Time will tell.
This will NOT be the highest scoring game overall. I can easily say that, since I'm not even eligible for the Modern Age scoring, and I have no prayer of getting the Largest City points. I think the winner is going to be someone who got through the tech tree very quickly, with high populations at those dates, got to the Modern Age fast and won a Diplo/Cultural victory at an early date. In fact, early true Diplo victory with lots of good relations with the AIs, early Astronomy, and tech trading/trade routes flowing back and forth probably will do very well if played correctly. I guess we'll have to see how everyone played it, but I think I'm well positioned for my usual silver or bronze medal here. Thanks for reading.
