50 BC: I started out by switching SOZ in Chichen Itza to building Stables with one turn remaining on the SOZ, as adviced.
1 AD: Joao completes the SOZ in Lisbon!
50: Finish Construction start on Currency. My cities are building stables and then starting to queue build war elephants and catapults and switching back and forth to minimize maintenance.
150: Finish Currency start on Meditation.
175: Finish Meditation Start on Priesthood. I decided at this point to go for Joao, Hannibal is safely locked in Pleased status unless some weird series of negative events unfold while Joao is only Cautious (HR bonus not yet obtained). Besides, Hannibal already has both HBR and Construction meaning I would face his army on equal footing while Joao lacks both of those techs. Hannibal can also offer better resource trading.
200: Finish Priesthood start on COL.
225: Trade Currency to Hannibal for Monarchy +40 gold.
250: Finish COL start on CS.
475: Finish CS, start on Paper. GS#2 is born in Lakhamba and I send him to Mutal to build an Academy.
520: Joao completes TOA in Lisbon. Wow, that's late! Now Lisbon contains the GLH, TOA and SOZ, neat.
600: Paper finishes, start on Education.
620: I DOW Joao and move against Guimaraes with a stack of 8 catapults, 5 WEs and 2 axemen. Unfortunately Joao culture bombed two of his border cities further to the east, eating up alot of tiles and forcing me to spread my army out along a long border to be ready for counterattacks and attempts to pillage my cottages.
Capital before DOW:
By not whipping I essentially kept a research of about 80-100 beakers in Mutal for the entire buildup-period and even during the war, allowing me to tech quite nicely compared to the slower-than-usual AggAIs. The tradeoff as we shall see, would be a slow war process after the initial successes.
640: Joao has aquired Construction by now but is still lacking HBR. I capture Guimaraes on my way to Lisbon.
660: GS#3 born in Mutal, I bulb him for part of Education.
700: Finish Education, start on Philosophy.
720: My army has healed up abit and moved on against Lisbon:
740: Something strange happened this turn. I was only able to kill 5 of the 6 defenders in Lisbon on the previous turn after my catapulting, due to lacking sufficient units. Joao was left with a half-dead Chariot in his city. What happened next is something I can't recall having seen before:
Joao abandons his supercapital. I guess it's actually not a bad decision, his chariot had no chance and he didn't have any reinforcements, but why not whip a unit and why leave a defenseless settler and galley in the city when they could safely have retreated as well?
In any case, a free worker for me on top a very lucrative city.
Not only the wonders but also an academy, several other buildings and a settled GG.
I paused the game here and pondered suing for peace. I had essentially diluted my SOD after taking Lisbon, and continuing would be a slower process. I had accomplished my primary goal by capturing the supercity already and Joao had 2 turns left on Feudalism.
I finally decided that I wanted to push on regardless. My economy was doing quite well, Hannibal wasn't able to trade with Joao since Joao was getting so backwards and wasn't leaving us behind in tech and Joao still lacked HBR.
I ended the turn by trading Paper and 50 gold to Hannibal for Music.
800: Philosophy finished and I found Taoism in Uxmal. Very late for that on Immortal indeed. There's been some warring going on abroad and the general tech pace have been considerably slowed by the AggAI setting. I start on Liberalism.
A birdsview of the empire at 800 AD (how do you remove the clouds?):
920: Hannibal steal Philosophy from me but he still lacks Education and I have 5 turns left on Liberalism.
940: The AP is built by a Hindu abroad.
1010: I finish Liberalism and pick Nationalism after considering Gunpowder for additional immediate military edge against Joao. I decide to go for the longer-term benefit. I start on Gunpowder.
1020: Switch to Monotheism to enable trade of Theocracy from Hannibal.
1030: Finish Monotheism, switch back to Gunpowder. I make a trade with Hannibal that benefits him far more but whatever I gain on everyone else at least.
1040: I finally capture another city after another 3 centuries of warring. I was a little unprepared for the sheer number of units the AI builds on immortal AggAI (never played with AGGAI on this level). Although I won most fights by far my units were constantly healing up from battle and hard pressed to advance.
After this I decide it's time to sue for peace. Joao has finally gotten around to teching HBR and my troops are spent.

Joao!
I get Calendar, 100 gold, 2 gold pt and a world map for peace and Joao immediately goes from Annoyed to Pleased (+4 religion, +4 civic).
Demographics after the war, doing quite alright I think:
The reason I can see Joaos research is that he used spies for alot of stupid sabotage/poison missions and the like, all my EPs are on Hannibal since my decision to go after Joao.
I'm considering getting Optics before I move on in the tech-tree but Hannibal is not willing to trade Compass or MC. If I go for extended peace which seems best I need to whip forges, universities and ball courts. After that I'm not really sure how I'll proceed. I need to finish of Joao but riflemen/grenadiers is a ways of yet and I don't know how effective Cuirassiers are when Joao's got elephants.