At this point I stopped caring about anything but killing off Montezuma. I didn't care about my economy. I didn't care about my research. I didn't care about growing my cities. I didn't even care about winning the game. I just wanted Monty to die, die, die, die, DIE.
As much as you may have felt you were playing out of irrational anger, I don't know that you really had any other options for dealing with the war with Monty. Giving in to the AP and stopping the war would have opened up the possibility of Monty becoming the vassal of one of your friends, and even if he didn't you still would have gotten the "declared war on our friend" hit from all your friends when you restarted the war. And the AP resolutions still could have come up in any subsequent war. The bottom line is that Monty had to die if you were going to have any chance of winning the game.
The real mistake was made in the previous rounds when you allowed Monty to expand unchecked. But that's water under the bridge now.
Moving forward, you're definitely facing a scary tech situation. Especially when you look closely and see where the AIs really are:
Hattie has Communism, Bio and Physics.
Zara has Fission and Electricity.
Hammurabi has Assembly Line.
The good news is that there are some differences between the AIs, so some tech brokering might be possible. Hattie doesn't have Rifling, so it might be possible to trade that for either Military Science or Democracy, and then trade that tech to another AI, etc. Then again Hattie may finish Rifling first making it worthless for trade purposes.
An Internet beeline may be the only option at this point. Checking the tech screen you're 12 techs away from Computers. The 11 pre-reqs basically fall into three lines:
- SciMeth->Physics->Electricity->Radio
- Steam->AL->Industrialism->Plastics
- Steel->RR->Combustion
(Of course there are some additional dependencies there.)
The bad news is that there are some other techs you really want to get that aren't on the list: Democracy, Bio and Refrigeration (for the UB) being the most significant.
It's hard to know what the best option would be for tech trading, but I would pursue Steam->AL after finishing Rifling. AL is expensive enough to get 1 for 1 trades from it, and the AI usually doesn't prioritize it. Hopefully Hammurabi will start building the Pentagon and won't trade it to anyone. At the very least AL will provide you with a significant upgrade to your military as well as a means to boost your production.
After AL is finished RR is only 2 techs away (1 if you can trade for Steel). Another good trading tech that the AI doesn't usually prioritize.
After that you'll need to see what you've gotten in trade and also what the AIs tech status is before deciding what to research next.
Regarding espionage, one of the reasons you're in such bad shape is that the AIs undoubtedly have jails and maybe even security bureaus in their cities, while you're relying only on courthouses. The good news is that since you have more cities than any of the AIs you can also get more EPs from buildings, if you can get the full set of espionage buildings in each city.
So you may want to look at founding as many cities as possible. In addition to the location mentioned between Cuzco and NY there are a couple more filler sites available. The coastal tile 3 NE of Boston can work 4 grassland, 3 grassland hills and a couple of coast tiles that no other city can work and the hill 3N1W of Pasadena can work 6 grassland tiles that no other city can work. Both should be able to at least pay their own expenses, so they're probably worthwhile.