(Apologies for any mis-spelling of city names!)
Opening
Changed University builds to Observatories, whipped the Ball Court in Mayapan and Library in Tenochtitlan, queued up Hindu Missionary builds in Texcoco and Tlatelolco, and began researching Corporation at 60%

.
Turn 1 | 1580AD
Mayapan: Ball Court > Hindu Temple
Hurrian: Ball Court > Cannon
Xukpi: Cavalry > Ball Court
East Shangian: Ball Court > Hindu Temple
Huananga: Library > Forge
Tenochtitlan: Library > Forge
Chaco Canyon: Granary > Barracks
Corihuayrachina: Culture > Forge
Uxmal: Wealth > Cannon
Tiawanaku and Tlaxcala: Whip Courthouses
Oxhuitza, Quirigua, Vitcos, and Vilcas: Whip Ball Courts
Turn 2 | 1585AD
Corporation > Physics, down to 50%
Cuzco: Granary > Wall Street
Oxhuitza: Ball Court > Cannon
Hurrian: Cannon > Cannon
Quirigua and Vicas: Ball Court > Cannon
Vitcos: Ball Court > Wealth
Machu Pichu: Ball Court > Forge
Tlaxcala: Courthouse > Barracks
Tiwanaku: Courthouse > Culture
Texcoco: Hindu Missionary > Observatory
No more Mr. Nice Guy ...
Joao's attitude drops to 'Cautious' as we declare war on his friend.
Steal two Native American Workers, pillage some fishing nets, lose a battle at 79% against a Knight in the field (in keeping with the tone of the turnset), spread Hinduism into Xochicalo. Citizens begin whining about fighting the brothers and sisters of the faith.
Calixtlahuaca: Change mind, and interrupt Library and opt for a Courthouse.
IBT
He's got Destroyers and Transports.
We lose a pretty poorly defended Chaco Canyon to Sitting Bull, while Ollantaytambo has an enemy stack at its doorstep.
Turn 3 | 1590AD
Mayapan: Hindu Temple > Cavalry
Retake Chaco Canyon.
Chaco Canyon: Courthouse
Attack Poverty Point: two Cavalry withdraw, two lose, the rest win.
Sitting Bull has a big stack with tons of siege outside Ollantaytambo, that have knocked out its defenses. Our eastern mini-stack of Cavalry head away from Mound City and veer toward Ollantaytambo.
Try to pick off a stray Native American War Elephant at 78%, and lose.
Having put a turn into Physics ...
Physics (interrupt) > Communism, however we need

for upgrades in light of Portuguese, and opt for 0%

.
Calixtlahuaca: Whip Courthouse
IBT
Lose both Ollantaytambo and Tlaxcala to the Native Americans.
Turn 4 | 1595AD
Xukpi: Ball Court > Cannon
Vilcabamba: Forge > Cannon
Calakmul: Maoi Statues > Forge
Retake Ollantaytambo and Tlaxcala.
Ollantaytambo: Forge
Tlaxcala: Courthouse
Elizabeth will trade Physics for Biology + our Map +

, however with no other trading opportunities any more, we don't pursue this trade.
IBT
We lose a Frigate and two Cavalry.
Turn 5 | 1600AD
Hurrian: Cannon > Cavalry
East Shangian: Hindu Temple > Cavalry
Quirigua: Cannon > Cannon
Hinduism successfully spread into Teohutican.
... and we pick up a Great General, who's sleeping in Hurrian awaiting 'instruction' ...
With some

in the federal reserve, we bounce back up to 50%

.
IBT
Joao drops eight units outside Calixtlahuaca; a Cavalry, three cannons, and four Grenadiers.
Turn 6 | 1605AD
Oxhuitza: Cannon > Cavalry
Hurrian: Cavalry > Cavalry
Vilcas: Cannon > Rifle
Upgrade Axe to Rifle at Calixtlahuaca - maybe we might do some defensive damage to Joao's invasion stack. Several cities near Calixtlahuaca drop their builds for Cavalry.
IBT
Lose Calixtlahuaca.
Turn 7 | 1610AD
Chichen Itza: Bank > Ball Court
Xukpi: Cannon > Cavalry
Huamanga: Forge > Ball Court
Teotihuacan: Library > Barracks
Tiwanaku: Culture > Forge
Tenochtitlan, Texcoco, Tlaxcala, Xochicalo, and East Shangian all get Cavalry whips.
Oxhuitza: Whip Cannon
Vilcas: Whip Rifleman
Our eastern Cavalry mini-stack head toward Calixtlahuaca.
IBT
Joao upgrades two Grenadiers to Infantry in Calixtlahuaca.
Turn 8 | 1615AD
Oxhuitza, Tenochtitlan, Texcoco, Tlaxcala, Xochicalo, and East Shangian: > Cavalry
Vilcas: Rifleman > Lighthouse
Turn 9 | 1620AD
Isabella is prepared to talk peace, but wants our Maoi Statues city to settle.
Mayapan: Cavalry > Cavalry
Vilcambamba: Cannon > Cannon
Manchu Pichu: Forge > Market
Retake Calixtlahuaca using two sui-Cannons, but dispose of the remaining defenders without loss.
[Call it a day, and hand-over]
Miscellaneous end of turnset screenshots: