Thank you for your detailed response. My main problem concerns item 16 in your list. In my games the AI is usually so far ahead in science and culture that they have advanced walls and units to easily defend against my cavalry. But never mind, I know that I am an at most mediocre player (despite my many playing hours) and simply not clever enough to make this work above level emperor.
There are a few ways around this.
If you struggle, practice on Epic or even Marathon speed first - this helps you in extending your window of opportunity to strike.
Also make sure that you fight within the city's borders after it flipped to your religion, that way you can leverage the benefits of crusade, whereas outside you are at a big disadvantage.
I would also look into this mod, which reverts the AI science focus that was introduced in the very last patch of civ 6:
https://steamcommunity.com/sharedfiles/filedetails/?id=2577006856
With this, you're playing "civ 6 as it used to be", and not in the mode where the AI goes mental for campuses.
If you can survive until stage 16, you're essentially doing it right.
You might have been very unlucky with the target AI, but this shouldnt be a showstopper.
Essentially, you only need to work on cutting corners to speed it up further if you feel that you are consistently too late at taking the first cities.
A good measure for knowing whether or not you timed it right, is to check for the combat strength of your target's cities.
If you are ready to invade with cavalry, you want your target to have a city combat strength of between 20 to 40.
20 indicates that your target only has ancient era units to defend with, 30 you can expect heavy chariots and swordsmen/horsemen (still doable).
At 40 you are a bit late, but it's still doable if you are good at tactical combat.
If the AI has something like 50 combat strength on the cities and you are on Heavy Chariots/Horsemen, you were too late and need to find a way to cut those corners for the rush.
Once you have taken a couple of cities from the AI, the game starts snowballing and becomes easier and easier, because you're essentially taking over developed cities and thus you catch up to the AI just by grabbing more and more cities.
Also feel free to grab Cross-Culture Dialogue for more "free science" as one of your beliefs, that one tends to help quit a lot to smooth out the initial science backwardness.
you can go horseriding before ironworking, not bothered if your nearest neighbours have built walls 
this is my religion, this is my light cavalry, this is now your former capital
