Thanks for the suggestions, I may try the COTM but I'm not sure that I will have sufficient free gaming time to complete it.
In the mean time, here are my notes from the first phase of this game (more or less covering the ancient and medieval eras).
I had what felt like a relatively solid expansion phase, but I'm not familiar with this difficulty level to know if I could have gotten away with more. I didn't want to be overly "greedy" by settling right up to my neighbours while I still had no significant military forces. I was also very wary of culture flips so I wanted to get temples in my edge cities before the borders joined up.
I was able to wall off both Egypt and Greece:
(I don't remember why I thought I could build the Great Library in this situation!)
I decided my strategy would be to get the most out of these super Legionnaires before they became militarily obsolete. I decided to make war on Egypt as they were going to be the most powerful local opponent, at least once they started using their Iron. I didn't want to attack Greece as their Hopolites would be a pain to push through. The priority was to cut off Egypt from using the Iron to my immediate West, and hope that they had no more.
I had been avoiding roading my own Iron to allow me to continue build Warriors cheaply. Between building Legionnaires and upgrading warriors, I was hoping I would have sufficient forces to take some of Egypt's closest cities at least. At this point in the game I was afraid that at this difficulty level, the A.I. would already have so many units that it would potentially be game over (I had seen impressive stacks of units being sent to round up barbarians).
Around 500 B.C. I declare war on Egypt and make a military alliance with Greece against them. I manage to take their Iron and raze several cities (clearing a buffer space) and start building settlers to try to take the now free land:
I don't remember if there was a pause for peace or not, but in the end I had conquered all of Egypt's mainland cities by around 30 B.C., though it turned out that they had some cities somewhere else. Their capital had the Great Library, capturing it brought my back up to date in technology, which I had fallen very much behind on. I make peace with them. The city Alexandria culture flips back to them at some point.
During the war, I got two great leaders, the first I used to rush the Forbidden Palace in Hippo Regius (North West, near Egpyt´s former Iron). The other is used to create a Legionnaire Army - which I somehow nearly lose when attacking a 1hp spearman!
I decided to continue my strategy of maximising the value of my unique unit, so I switched to Monarchy to allow me to sustain war for a long time to come. I take some time to rebuild my military and improve my core cities, and around 500 A.D. I decided to attack Greece (I was considering also India, who were weaker, but I lacked the required naval units).
I lose lots of Legionnaries as Greece have good defensive units and also the terrain is very unfavourable (jungle slows me and gives them defensive bonus). This is exacerbated by the fact that the Great Library has made Legionnaires obsolete so I can no longer build them, with Medieval Infantry being slower and Knights being more expensive. Fighting a two front war against Greece (on either side of the inner sea) divides my forces. I also lack sufficient defensive units, so Greek counter-attacks keep killing off my valuable strong attacking units.
This meat grinder continues on for a very long time, to the point where I'm down to relatively few units and Greece still seems to have strong stacks, so I sign a Military Alliance with Babylon to distract Greece and take some heat off my front. This works as intended, I eventually achieve a critical mass on both fronts and break through the problematic terrain and start steamrolling the Greek cities, with my troops meeting in Athens. I conquer Greece by around 730 A.D., and around the same time I conquer the last remaining Egyptian cities.
Elsewhere in the world, the Zulu appear to be collapsing too. The other A.I.s are generally in Republic and out-teching me once again. At this point I am considering triggering some kind of world war to try to slow everyone down, ideally against Germany who are the strongest, and including Babylon, both to drain their forces and to avoid them looking to attack me.