As a SCI civ you get a bit of a boost entering the Middle Ages.
As already mentioned, I was lucky enough to get Feudalism and Monotheism after gifting and trading with Persia. All I needed to research after that was Chivaly.
However, since Iron was not easily availble, I kept the research slider fairly low and used the cash for short-rushing Horsemen with which I started the conquest aiming, among other things, for getting control over some Iron. I tried to time the discovery of Chivalry with the connection of Iron.
So what are you doing to keep them in their place; hack some jungle for more space, capture some cities or just develop in place??
All of the above, but with priorities. Obviously, first, I developed the original core. First for growth under despotism, having all Wheat tiles irrigated. Then for production during the Golden Age, having all tiles produce at least one shield before the GA started. I improved the land as far as the Hills in the north plus a road to the Dyes in the jungle, then sent nine workers to build a war road towards Persia.
Second was to start the conquest of the nearest and most promising target, Zululand. They had The Pyramids, unfortunately also The Great Wall. They were easiest to reach (using Galleys, I peaked 18 of them). They had a reasonable location for a second core. The Iron in Carthage behind appeared to be the easiest to connect. I didn't have the resources to send Settlers, Workers and defenders over to claim the mountain Iron on the rocky isthmus north-east of Zululand, and I didn't fancy reconnecting Iron on a mountain.
Hacking Jungle I did very late in the game, first using the Workers that were left, then using the nine from the jungle road gang too when they were finished. I sent some to road Zululand as well, which was more important. A few Workers were joined to towns after they got an Aqueduct in order to improve the economy. Hacking Jungle had the lowest priority.
And how does your Middle Age go? Forbidden Palace anyone? How about Palace Jumps?
I did build a Forbidden Palace in a core city on the river. It was ready in 530 BC. The same turn, Rome declared war on us. The Zulu had declared a few turns earlier. Also in 530 BC, Bowmen and Horsemen just failed to capture Zimbabwe, triggering the Golden Age in the process. The city, with The Pyramids and The Great Wall, was captured the next turn. The following turn again, Babylon reached 30 spt production and I was churning out Horsemen seriously, but also Galleys for the transport.
At the end of the Golden Age, I finally connected Iron and could start upgrading. Zululand was reduced to insignificance. At this stage, upkeep costs were staggering, so I build Knights stone by stone and upgraded Horsemen as I could afford it. I didn't strike the balance quite right (stuck finishing Knights when I had the funds, and no 60-shield improvement to use for short-rushing because of The Pyramids and the religious trait) and suffered a little dip in available units at the front.
From there on it was just standard Knights beating all to crumbles. I used a two-pronged approach with the main force going through Zululand, Carthage, India to Mongolia and later a smaller army directly from the first core going to Persia, Rome and the collection of useless cities in the Jungle. After the Golden Age I disbanded some Galleys towards Knights in the first core and kept only one complete ship chain shipping over two units per turn.
What didn't happen, evening out my good luck with the technology bonuses, was the emergence of a Great Leader. Not until 330 AD the first one came, in an awkward location, and I could establish my long-prepared second core in Hlobane through a Palace Jump four turns later. Too late to make a difference. As mentioned, Babylon was my largest and strongest city, so starving and abandoning it was not an option.
I also didn't get as many happy war declarations as expected.
Notable was the spunkiness of the AIs. India and Mongolia fought back bravely with several War Elephants and Keshiks. There were often three defensive and one offensive unit in non-capital cities. Perhaps this was partly due to the predator obstacles. Perhaps I had simply been to slow with my conquest.
They also researched extremely well: Engineering, Printing Press, Invention. I wasn't able to extort Engineering until 300 AD, which hampered my troop movements somewhat, since there were several rivers to cross.