War With The Aztecs
This invasion was easier than my invasion of the Inca island. But quite time-consuming - the Aztec military was large.
In 1615AD I landed my first units on the Aztec island:
I also rushed my first few Cruisers at this date. I generally avoid sea battles but the Galleons floating around, particularly Incan ones, were interfering with my Transports. My Cruisers slowly took care of that problem.
In the next four turns I landed more troops and I spread my invasion forces out, occupying nearby tiles on turns when the Aztecs left them empty or poorly defended. At the start of 1635AD:
In 1635AD I investigated the Aztec city near my landing force. (It sure was nice to be able to spy at last!) It had 71 defenders, the strongest being Riflemen. I had 34 armies which could attack, and about 100 artillery. After bombarding I figured my armies could average 2.5 to 3 kills each, enough to take the city. So I attacked. It worked fine, I razed Tlacopan. This would allow me to settle my beachhead at an ideal location.
I decided to make a long Funnel Of Doom this time. It would be overkill for the Aztecs but it seemed an interesting excercise. I wanted to confirm that the AI would send units into the Funnel even when it would take many turns to reach my city. In 1640AD I settled to claim silks and formed the FOD:
The arrows show the paths the Aztecs can follow to reach my city without attacking an army.
The Aztecs filled the funnel over the next few turns. Their arrival was a bit staggered because they didn't have coal and therefore didn't have railroads. They spread out further as they entered the funnel - faster units raced ahead, units wounded by potshots from the funnel walls stopped or went back a bit to heal.
I couldn't connect silks yet because of the Aztec city northeast of my beachhead - its cultural region was blocking my beachhead from connecting to the open seas. In 1660 I razed that city and finally had a seventh luxury connected.
This Funnel Of Doom turned out to be serious overkill. At 1650AD the first Aztecs reached my city and 14 died attacking it. Next turn 17 died, then 29, then 50 at 1665AD. Each turn I also killed a fair number of units near the entrance to the Funnel, averaging about 60 per turn. Although the Funnel was finally ramping up the number of Aztecs arriving at my city was far less than my defenders could handle. I'd whittled down the Aztecs far enough by 1665AD to figure that their entire remaining force could not take my city unless they all reached it on the same turn. So I dismantled the Funnel, opening access to my city:
The Aztec units would still arrive at staggered intervals because many of them had been in transit in the Funnel. In 1670AD 77 Aztecs attacked and died. Then came the big turns. In 1675AD 183 Aztecs attacked and died. At the end of their attack my strongest defender was still a mid-yellow Infantry army. I also destroyed 63 Aztecs in my part of that turn and lost 1 Cavalry doing so. I think that sets a new Civ record for me: 246 enemy units destroyed, 1 unit lost! In 1680AD another 103 Aztecs died throwing themselves at my city and I destroyed another 109, losing 3 Cavalry to do so.
At the end of that turn (1680AD) the Aztec forces were down to 197 surviving units. Less than they'd lost in each of the last two turns. I could pretty much ignore them now. I'd already started sending out Cavalry armies to raze their cities some turns before this. In 1690AD I razed the last two Aztec cities and they were out of the game. Their remaining 154 units poofed out of existence, leaving the island to me.
My military is now heading for my remaining rivals. None is very strong. China is by far largest and her military is only considered "average" compared with mine. I don't expect any large challenge in the rest of the game. It will be a matter of picking off my opponents and milking the best land as quickly as possible.
Milking
In 1610AD I traded China Refining + Steel for another 20 turns of fur supply. I should be able to stay at eight luxuries from now on except a few turns at the beginning of my invasion of China.
In 1630AD I reassigned all of my taxmen to be scientists and began serious research. I abandoned my one-scientist research of Flight which still had 16 turns to go and started on Sanitation. Learned Sanitation in 1650AD, Mass Production in 1670AD, and Flight in 1695AD. I've built a number of Hospitals now and will continue researching as quickly as I can until I can build Mass Transits to go with the Hospitals.
When I destroyed the Aztecs in 1690AD their island looked like this:
My transports had been bringing over settlers and workers during the war, preparing for this moment. I disbanded cities in poor territory at home and the builders sprang to work on the island. I disbanded some military units, including most of my artillery, to speed development. Three turns later at my current game date 1705AD the transformation to a modern Iroquois province is well under way:
At 1705AD my score is 27660.
Thoughts about Funnels and Armies
The Funnel Of Doom I set up for the Aztecs was major overkill. I think that if a player has time (no immediate threat of losing, e.g. to culture), a Funnel with about 1/2 this strength (in terms of defenders in the city and spare Cavalry armies for attacks) could handle an AI military about twice the size of the Aztecs and containing a significant number of Infantry, and dealing with an AI with railroads. This technique can make a joke of the odds facing the invasion of an isolated Sid AI.
I think that a faster variant might be possible for invading and destroying a large AI. I could have created two separate four tile funnels to my city, one on each side following the coast. On alternate turns, "close" one funnel by moving a Cavalry to its tile nearest the city, and "open" the corresponding tile in the other funnel. I think the effect of this would be that the AI would move all of its forces back and forth between the two funnels, never reaching the city. It might be necessary to destroy a few injured fast units which stay in the wrong place each turn but basically I think it would work. With the bulk of the AI's forces kept busy this way, the human could send most armies (those not making up the funnel walls) out to raze the now relatively undefended enemy cities. The Aztec cities had many units (e.g. 71 in the city I first attacked) when I first entered their land. But as soon as they had a target to attack just a few (typically 4) defenders were left behind in each city. A group of 5 Cavalry armies can be expected to raze such a city even if the defenders are Infantry. An extra trick would be required to raze enemy cities near the beachhead - the AI tends to withdraw wounded troops to them. I think a few carefully placed armies along with some pillaging could isolate one city at a time from being used this way. The end result with an approach like this would be to destroy the AI without ever engaging most of its forces. Just make them go "poof" instead

One risk with this approach would be if there were an isolated fragment of the same Civ to deal with (e.g. a nasty one-tile island) or if there were a wandering settler. I think the settler problem can be avoided by attacking only at a time when every tile in the world has been claimed by someone.
I hope that the final patch for C3C includes some changes to depower army tricks like these. They exploit the AI's predictability to an unreasonable degree. This isn't just for Sid level. Sid level is the stress test where we push vulnerabilities to their extreme. AI improvements for weaknesses exploited at Sid level will make for a better game at all levels I think. Changes I'd like to see:
1) It should not be possible to rush army builds with cash.
2) Change the AI to attack armies in the open, prioritizing armies sitting on resources.
3) Change the AI to build armies.