Interestingly, the nukes weren't much faster than the way I went about it. I had already taken Sally and Lincoln as vassals by about 15 turns before your victory. At that point I would have loaded up the ships again (combination of tanks, infantry and a few paratroopers) and sailed for Paris. Because it was

, each war only lasted one turn. I had also just been elected the head of the UN and was waiting to see if I was going to win the diplomatic victory on the first try.
As far as advice on moving up to noble, I'll throw a few out for you:
1. MORE WORKERS. LOTS more workers. Workers are one of the most powerful units in the game. Do not underestimate them. I set Tiwanaku to auto-build workers (since it could generate one per turn) and had it make a total of 15. I just set them on Automate (which you should
not do) because there was just so much land still left to improve. I think there were unimproved grassland tiles around your capital. Advice for Noble: Don't do that. Always try to either have your citizens working improved tiles, or make sure you pull them off the unimproved tiles and make them specialists.
2. Don't forget to take advantage of whatever it is your civilization is good at. For example, as an industrious civilization, it takes half as many hammers to build a forge as it does for other civs. However, you had a few cities without a forge. (Forges are very useful buildings. Not only do they multiply the amount of hammers your city generates, but they also increase the happy faces when you have gold, silver and gems.) If you are industrious, half price forges are a big advantage for you, and you should not only build them in all your cities, but also seriously consider attempting to get Metal Casting from the Oracle wonder really early in the game.
Similarly, if you are an organized civilization next time, don't forget that you get half price courthouses, which will allow you to expand faster early in the game. Many people will try to get Code of Laws from the Oracle in order to take full advantage of the organized trait.
3. Try to focus at least one city on building your military units, and a second coastal city on building a navy. Even if you were planning on being peaceful, you were in a position to build a powerful army and navy by really only using two or three cities.
4. Try to keep your civics more in line with what your empire is doing. With all of those towns and all of that commerce, it made a lot more sense for you to be in Free Religion, Free Speech, Free Market, Emancipation, and Universal Suffrage.