Civilization offers many paths to each type of victory. You love war, warfare, combat, and, in general, being a thoroughly disagreeable fellow: there's no reason you can't use this to make friends.
One way to the love of city-states is through war on the city-states. The way is convoluted, but making peace through war generally is.
Here's how to get one city-state to love you:
- Capture the city-state through war (either against the city-state itself, or with the city-state allied with another civilization that you're at war with). You'll get some lovely faith, culture, and/or gold, if you've picked up your favorite Honor-Aztecs and grabbed the right pantheon/religion/policies.
- Make sure another civilization gets the captured city-state. Either give it to them outright, lose it to them in a war, or make thousands of coins by selling it to them. (You might see something peculiar: the AI will usually reject trades that are too good for it. So if you offer them Vancouver and ask for 1000 coins, they might reject the trade, but if you offer them Vancouver and ask for 5000 coins, they might accept it. I've never seen them reject a gift where you ask for nothing in return, though.)
- Go to war with that civilization, recapture the city-state, and choose to liberate it instead of puppeting or annexing it. The city-state will now love you, and be your ally.
You can repeat this, and collect allies. If you attack the city-states individually, then at some point, most of the city-states will unite and declare permanent war against you. I'm not sure if a liberated city-state that was once at permanent war will forgive you or not, but I think they would. Of course, this convoluted scheme can be made simple if another civilization has already captured a city-state: just go to war, recapture the city-state, and liberate it.
Note: this technique is unreliable. Some opponents will just liberate a city-state when you give it to them, either because they can't afford the inconvenience of owning another city or they really like the benefits of having a city-state ally.
The only way to a cultural victory in Brave New World is through Tourism, and the only source of Tourism is Great Works: I don't dispute this. However, your incredible culture income (via your Honor-Aztecs) will make it easy to pick up the Aesthetics social policy tree, and that tree is a huge source of Tourism. Simply starting Aesthetics will give you Great Artists/Musicians/Writers faster, and finishing it will let you purchase Great Artists/Musicians/Writers with Faith in the Industrial Age, which your Honor-Aztecs are earning by the boatload.
Even without your gold, culture, and faith bonuses, you can win a Tourism Victory through simple war. Great Works can be captured from opposing civilizations when you capture their cities, reducing your opponent's future Culture and giving you Tourism. And if you eliminate a civilization entirely, then you don't need to beat their Culture at all; you only need to apply your Tourism to existing civilizations to win. So when Napoleon is the only remaining opponent that you aren't culturally-dominant over, just kill him and you'll take your cultural victory.