The most obvious fixes are:
-play a game where you meet another civ before you have 20 colonies
-make the large empire penalty scale better + nerf patriotic (which i think is on the list along with making research cost scale with mapsize)
End of EleventhStar's quote
1. He's on course to hit 20 colonies by around turn 18. No AI is in any state to do anyting about it at that point, and as noted elsewhere, he's still able to trigger the 50-turn Pragmatic peace option whenever he likes.
2. LEP scaling, and therefore patriotic, have no real impact here. He's not gotten to a 'big' empire yet in immense/abundant terms, and increasing LEP nerfs the AI more than the player. The trick is NOT simply punishing the player for having a big empire - if you're going to include big maps, then big empires need to be playable. The trick is making a big empire harder to achieve. You need a mechanic which produces a 'sweet spot' for growth rates, so that expanding too fast causes an issue, not simply handing out meaningless punishments for having the audacity to build a big empire in an empire-building game.
LEP isn't part of the solution; it's part of the problem. You can get round it by just not bothering to build farms; the population division effect is far, far, far more damaging than the effect of any number of LEP penalties - and what's more, it doesn't limit the RATE of expansion - it just produces an artificial cap on the number of worlds that you can support. Increasing it won't help, since your best strategy remains spamming colony ships as rapidly as possible until you reach whatever the cap turns out to be.
We need something which makes new planets a liability until they've been built up. That is the only thing that will make any early-game strategy other than colony spam viable. There's two basic options for this - one is increasing maintenance levels from undeveloped colonies, the other is forcing new colonies to 'import' food from somewhere or else lose population until they go extinct.