The problem with Sumeria is the 160-shield cathedral. This is not easy to rush. If you are using the ToA, you now will not be rushing either the cathedral or the university. If you are not using the ToA, then the cheaper university will be nice, though. If you can rush the ToA, you could expand like crazy, research to education, and then decide whether keeping the temples or building them anew and rushing universities is the better deal.I may be talking myself into the Sumerians for 100k games, because a 60 shield temple is a lot worse than an 80 shield temple. You only need 3 dead for a temple and 2 dead for a library with the Sumerians.
If you aren't going to use the ToA and you are going to use Babylon (giving up the agricultural trait), you might try PTW for large and huge 100k games. Then you only need 100k to win. I've done this with some success (at least I'm no worse than with Conquests). You can't pop-rush in Feudalism, but you can get to nationalism and draft as a republic, or you can go to communism to pop-rush. (Be aware that basically every city will be totally corrupt in communism, so you will not be building anything by hand anywhere).
Yes, you definitely need as many cities as possible. If you had fewer than 200 cities, that is your problem. ICS everything, although you should give the first couple of cities a bit more room. At the end you may need to build cities to give to your opponents to avoid hitting the domination limit. Once a city has build its culture, pop-rush settlers from it (and also steal its food for other towns).
And, yes, my strategy for doing harder 20k games is to play archipelago, looking for an isolated island with water. I leave my capital empty so as to draw attackers to it in hopes of generating a leader, which sometimes happens. With an army I can invade the weakest AI and progress from there.