The whole world is Hindu. Montezuma sent a very obvious attack stack towards me, that I fended off by demanding money to lock in a 10 turn peace treaty. Then he peacetime-vassalized to Hannibal. (?)
Yes, that's the Palace going up in Barcelona. I had a really abusive idea. Let's stack up Bureaucracy (+50% "food" in my highest hammer city) with the Globe Theater. Behold!
It has 243 hammers in the food box. Its hammer surplus each turn is greater than the half-a-box consumed by the granary. I want this city to hit size 100 by the end of the game. It will of course get the National Park to fix health.
GPs #4 and #5 were both extra Engineers. No need to rush any wonders with my lead. So each settled in Barcelona -- his multiplied hammers will support two more specialists!
The Great Artist from Music kicked off my first Golden Age. Doing that sooner for the crazy kick up the hammer growth curve might have been even more fun. But now is still a good time, some cities aren't up to size yet, and the commerce comes at a good time to build key wonders in Notre Dame and Angkor Wat.
Yeah, Angkor Wat is yet another broken item here. It makes priests *add* "food" after hammer multipliers, on top of their coin and free GPP.
Progressing through the Renaissance, my tech order was Nationalism (go go consecutive Golden Ages) - Constitution (definitely want Representation ASAP) - Education (perhaps a bit belated) - Banking - Printing Press (late, almost no villages) - Replaceable Parts (Lumbermills!) - Economics (Free Market is +4 or so production) - Astronomy (the Colossus can't last forever, now we need observatories -- oh and also galleons.)
The galleons were to grab two island cities: one for spices, and one just because I could and to grab a Mining Inc resource.
Yes, that is 58 commerce-production on the first turn of existence. Amusingly, the huge cities at home help provide trade route income to overseas cities! And amusingly, it's actually correct to build something else before the granary, because the granary will still be finished before the food box even gets to half full.
Divine Right posed an interesting question. The Spiral Minaret does pay back more than the research cost before it expires. But I planned to go Free Religion eventually, largely for the happiness, canceling out Spiral. But - Free Religion is another reason to research Divine Right, since having Islam will make for 2 happy per city with the temple. I went for it.
Let's think about corporations. Three corps are off the board: Civ Jewelers is off the spaceship tech path, Aluminum Co is nothing with only one coal, and CreateCon is far behind Mining Inc.
Mining at +10 hammers (+20 after all multipliers) is an obvious play. Or is it? My limiting factor on city size is the happy cap. Even with all the resources, Free Religion, Hit wonders, and temples and cathedrals, the happy cap will be about 45 at most. With factories and power and railroads and huge Golden Ages, my cities are already over 90 hammers each. Mining Inc is unnecessary.
Sid's Sushi is totally not worth it! Per city, it would convert about 6 gold to 3 food, which does come back to 6 beakers after multipliers, but that is not worth the expenditure on executives. Cereal Mills fares little better. For once, Standard Ethanol is the best rice-consuming corporation.
What about State Property compared to Ethanol? The corp is +21 beakers/city, with its maintenance about netting out against the HQ income. Multipliers take the corp to +40/city or about +500 total nationwide. State Property would save 50 (75 after inflation) in distance maintenance, plus add about 30 multiplied to 60 research from workshop food. That's 135 units nationwide. Its hammers will help a little bit but not enough to make up that big difference. So figuring the Communism research cost of SP as about a wash against the executive cost of Ethanol, Ethanol is the winner.
Let's also think about civics. 
What about Hereditary Rule for happy over Representation? Rep doubles specialist productivity, so for HR to match that, it must create happiness equal to my original number of specialists. That actually might happen! But I am NOT building and fortifying 45 musketmen per city.
I got great use out of the Globe Theater and National Park, but some of the other national wonders were hard to leverage. The National Epic got put off for a very long time, since any other city even with it could not outpace giant Barcelona on GPP. I then realized that the NE could go very well in an Ironworks city for specialists. :D But then also realized that Oxford had to go somewhere and the Ironworks city is the best place for Oxford too. But then also realized that the Ironworks is overkill, just like Mining Inc, the city will crash into the happy cap first.
So the best use of the Ironworks is actually to get a hammer-poor city up to size. The best use of the National Epic is just to put it in Madrid to multiply its wonder GPP. And the best use of Oxford is just my second biggest city, and give it cathedrals for happy.
Industrial Age research path: Gunpowder, Chemistry, Steam Power (beelining to Levees, more growth insanity), Corporation - Assembly Line (soonest I've ever gone here), Steel - Railroad, Scientific Method (late) - Physics - Electricity - Radio (must get the Hit/Eiffel happy wonders up ASAP.) I did build coal plants. Obviously +50% hammers easily outweighs -4 hammer-food from unhealth.
I sandbagged Liberalism until Radio, both because I wanted Radio sooner and because it was now time for Free Religion. So much for my expected research slowdown. 20 Rep specialists per city drove research at a ghastly pace, hitting 2 or 3 turns for most Industrial and Modern techs.
Size 63 city at 1500 AD, if anyone's counting for the honorable mention. Texcoco down there was assigned to me in an Apostolic Palace vote, speeding up the inevitable flip.