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...