1. Knights suck, because Cuirrassiers can be reched in about the same time via bulbings and Lib. Very late, I had a game where I dominated the map with Cataphracts, but my advantage from early on was that great on the map, that also could have dominated with basically every other unit, Mass-Cataphracts were just the fastest way, becuse I got all tech from the AI, couldn't self-tech past Civil-Service because of too many troops etc.. Those are extreme exceptions. In a normal game, when someone is trying to build a merga-vassal-empire, you bribe him to peace and steal the cities of the weakened defender after the mega-civ has lost enough troops. Maybe bribe his also-mega-civ friend from the other side of his empire onto him at the same time, that should stop him from ever becoming dangerous.
And if I got Ivory, I really stop after building 3 cities. Elepults are simple the cheaper way to get larger, better developed cities. I'd maybe think otherwise though, if my only target of choice were Ragnar or Mehmed. Then I'd probably again try to let someone declare war on them, and march into the back of their empire when their troops are gone.
Deciding factor for Lib -> Rifling i. e. is "no Iron" and Steel combines very well with lots of weak 1-move-units, like Axes, Swords, Maces, Elephants etc.., so Lib -> Steel is a powerful option also, when having been very successful at early war. That's a different scenario that I talked of though, I morely talked of using Rifles or Cannons as a breakout weapon, because there's nothing more powerful than mass-drafting Rifles or take anything and add Cannons to it. REXing to 6-9 cities will make it very hard to get Liberalism btw.. It's possible, but really need to be a well trader and make good use of bulbs. Liberalism with 6 cities is much easier, Liberalism with 12 cities I currently don't remember having ever achieved, think 11 was my maximum.
It's imo all about the map and how strong you really are. If you get offered Ivory and wouldn't use it, you'd deny yourself Elepults, and Elepults are while a little more difficult at least as strong as Cuirrassiers but because earlier much better. I think you need to work more on preparing the war. Watch out for happenings i. e., that one Civ declares war on another. Then look, whom both sides could bribe, and gift everyone of them a large techt, so they actually can. BAM, 10 DoW's next turn, world war, GG. Or when you DoW anyone who is your friend, bribe him into Caste, and you'll have 0 problems with reinforcements. And don't forget to save your gold-begs for the war-scenarios. AIs have a high chance to backstab on the 1st turn of war, but 10T later, chances are below 10%. Learn to be in control of the diplo-game on the map, ideally, you mostly backstab targets whom's stacks are far away fighting the ones of others and you don't get DoWed once, because everybody is already fighting, or because you got perfect relations. Things like that are one reason, why I like Oracle so much, because it offers a huge additional tech. That tech can easily be +4 with all Civs or bribe everybody against everybody etc., so even in total war games, I always try to snatch it at about 1800 BC, when I traded all pre-requisuites, looked, found that only 1-2 civs have Priesthood, and then researched Priesthood myself and chop-whipped it in 4-5T, maybe also only 1-2T because I prepared Chops for exatly this opportunity.