I have once again fallen into the same problem.... probably as a coping mechanism the AI gets bonuses it seems because of proximity to the player.
When you pull ahead you start noticing.... the AI with the highest scores are ALWAYS your immediate neighbour, he either ties with or surpasses you in tech, he becomes irrationally aggressive and there is only one of them. He tries to bring you down and basically forces you to either destroy or vassal him.... the other AI progressively jump on the bandwagon and by the time you have delt with this threat.... it's basically game over because no other AI stands a chance any more.
You start noticing this because sometimes another AI far away becomes the new golden child who suddenly is tech competitive but most of the time it does not stand much of a chance anyway. At the same time the AI suffers due to the costs of expansion so you notice it barely expands at all and then there are explosions of wars and settler activity.... depending on player performance. I wonder why the devs decided to try and nuance it this way instead of just giving all of the AI (or at least a third) boosts.
I did not even make it past cannon this time before I basically won the game. The AI simply does not expand the way it should, probably because it needs to funnel resources into useless military units it does nothing constructive with. And then there is the build then bankrupt/disband loop.
I had to think about why the AI falls off in the late game - obviously the early-game strength is annoying (as you said in your previous post - the AI's only chance at winning is to wipe you off the map before it can't win). But there's one specific thing the early game does that the late game does not, which is...
...Unit Counts.
The AI actually *isn't bad* at pinning down units, using flanking, mobility, etc. Yes, it seems to run away at times for no reason. However, what functions as either an advantage or just a normal baseline for the AI in the early game falls off later on because there are SO MANY units that that pinning a unit, for example, becomes impossible. Additionally, the ridiculous movement speeds of some units (Tanks, Railroads) allow the player in particular to gain advantages in combat in places he otherwise couldn't, and the AI can't keep up with it.
Essentially, if I had a suggestion to make - it would be that unit counts should remain fairly static throughout the game, right through to the Modern era. If the player can only defend so many flanks at once, then the AI has some maneuverability available; if the player is winning decisively, then a multi-pronged attack from several Civs has the potential to do real damage. And as previously mentioned - movement speeds need to put on the brakes, because with Railroad tech in particular it's just too easy to defend everywhere simultaneously.
This is just a start, there's likely more - but you've got to start somewhere.