Okay, after much delay, here are my four screenshots, again, all on Regent:
1) Macedon:
This was my first win on this Conquest after losing as Rome twice. I went straight through Iconium to Antioch with my army, then lost Iconium. I then sent my army down to Gaza, which Persia had taken from Egypt. I took Gaza and slowly moved my way back north. Meanwhile, my other troops took the three northern cities of Asia Minor. I got two more armies from this, and in one turn I had them all attacking cities - Antioch, Melitene and Iconium. Iconium was a breeze and Melitene was hard, but in the end I took all three. I then worked my way down the Euphrates all the way to Persepolis and Susa, then finished off Persia near the Caspian Sea. I then conquered Egypt, which put me at enough for a Domination victory 1 turn before the end.
2) Carthage:
As Carthage, I began by getting Macedon on my side. I then took Messana from Rome, reinforced each of my three islands and Spain and attacked the Italian penisula. After a while, I fought my way to Rome (with my army) and took it. It was pretty easy from there on out, as Rome had wasted a lot of time on the Celts. I also took the south half of Egypt, as Persia got the rest before I could. Persia then also conquered a weakened Macedon except for a couple cities that Rome had taken from them. I drove them out of Gaul, then decided to attack Goths because Rome had taken a city from them and all of my Heavy Cavalry were there. After defeating the Goths, I had enough to count for another Domination victory, 17 turns from the end. Persia was ahead in points, though.
3) Persia:
In my Persia game, I already had a pretty good idea of what Macedon could do, so I reinforced Inconium with many Immortals. I also focused on building many settlers to populate the middle of Persia's "ring of cities" and to the north. I eventually took Sardis, lost it, took Miletus, then took Sardis again until I got to Byzantium. From there it was simple and Macedon was gone. I then turned to Egypt, defeated them quickly, and finally started into Scythia before I won 37 turns before the end, by far my best game.
4) Rome:
In my third Roman game, I finally figured out that you have to conquer Carthago early before it is too well defended. I did so, and slowly took more cities of Carthage's. I also declared war on Celts in the fourth turn or so and took Massilia, then offered peace. Carthage was a pest with Massilia and it changed hands seven times. After defeating Carthage, I turned to Celts, and even took their city in England. Scythia took most of the Goth's cities and I took the last one to finish them off too. Meanwhile, Persia started to gain ground on Macedon and I declared war to get what I could get. I conquered all the way to Byzantium, which they got. Then I attacked Persia and took a couple cities to get to domination with 3 turns left. In the end, there were only three civs left: Rome, Persia and Scythia.
Sorry for my lack of word choice in those descriptions...
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of this scenario: when the road is free Carthage goes to Rome via Suez and around the Black Sea (because Byzantium is in the way). Actually, for Carthago's sake the 'Suez' passage should be blocked by Egypt, so that Carthago will go by sea. 
