I am not that good at war because I have not practiced it much. That being said and taken with a few grains of salt, you could try different plans. Instead of taking one city at the time, maybe you could fight to control at least half or more of their land, perhaps all of it, before you take any cities. That means, first you are going to defeat their standing army and that stage of the campaign can probably be started many turns before you actually plan to invade. When you do invade, you probably want to pillage everything that gives them production and happiness and gold. Districts take time to repair so, you may or may not want to pillage them. It depends on how long it would take to control their land. Improvements can be repaired very quickly if you have a few builders and repairs don't take charges.
Taking control of the land first means you have to deal with the walls first, everywhere you plan to occupy. That means you need enough rams or siege to disable the walls. Say you are in the classical era, and they have 5 cities. Suppose you start the war at the beginning of the classical era, and it goes well. Once you invade, suppose you have 3 rams, and you have enough units to attack three cities at once. If you can get the walls down, you don't have to capture the cities immediately. Yes, they will produce units and what the AI will do is try to produce a very advanced unit. If they don't have resources, they will try get produce a pike, if the game is still early. That is how the AI tries to deal with prolonged wars. They try to tech out of it. So, can this sort of plan work? It just depends on whether they can get a tech advantage on you. If they get a pike, a knight, or a man-at-arms and you have swords and archers, you will probably have to retreat.
Well, if you can take enough cities at once, you can probably put your governors into the cities that are closest to their remaining cities. I don't think you have a lot of flexibility with what your empire can accomplish early in the game. That means that if you try to conquer a neighbor and you fail, you probably are so far behind on your own development that you might as well resign. You really need to be successful in the early game. Later in the game, you can probably fight a war and in other parts of your empire be developing your cities because by then you probably have plenty of them.
I wish I was better at the game. I really don't know if a larger scale attack can work in the early game. I hate having to deal with city flipping too. An alternate approach may be to move through the enemy empire as quickly as possible and flip the entire empire to free cities. Then you can go back and capture the free cities when you can, but even if you don't do that quickly, at least the AI empire would be eliminated. Free cities won't mount a concerted effort to defeat you and can't win the game. So, you don't need to capture the whole world. You just have to free it and then capture the original capitals. If you are going for this strategy, perhaps you could try towers and just go over the walls and move to the next city as fast as possible. That might be problematic for your lines of reinforcement though since free cities spawn couple of defenders.
If you find any larger scale strategies that work, will you post them?