Well, I was going to take a break from Civ, but some of the posts in this thread gave me an idea I just had to test out. I think I've actually made a real theoretical breakthrough here, which is exciting.
I've done some experimenting with hybrid Liberty strategies, where the finisher is saved for the endgame, and it's never quite felt right. The issue is that the right side of Liberty is really hard to pass up. Meritocracy is the only happiness policy in the tree, and I don't think you can go without it. Representation is also a big difference maker once you're talking about 6+ cities -- it means faster Rationalism and something close to 2 extra policies over the course of the game. Choosing which of these policies to forego always seemed like a dilemma without a right answer, and it made the overall strategy seem fundamentally flawed.
However, there's one more option that's often forgotten, and that's the one I chose for this game: take all of Liberty EXCEPT Collective Rule!
This allows you to pick up both of the crucial right-side Liberty policies, at the cost of a slower start. However, I find it's quite easy to get enough cash to purchase two Settlers if you're diligent about pillaging the AI. Could that be enough to go to 6+ cities without Collective Rule? Apparently, the answer is yes.
I chose Egypt, banking on Burial Tombs being awesome and the UA giving me enough hammers to hard-build a wide NC in reasonable time. My starting policy path was Liberty opener --> Republic -->Piety opener --> Organized Religion --> right-side Liberty.The main theoretical benefit of this approach is great person maximization -- it's easy to generate enough faith for 3 Great Scientists, and the Liberty finisher tacks on one more for the endgame without any counter-bumping issues.
Key timings & details: finished 7-city NC on t89. Education at t101. Scientific Theory at ~t142 (one bulb). Plastics at ~167 (two bulbs, with Fertilizer detour). Finished LToP at ~t142 (all AIs were warring heavily, also I'm extremely lucky). Tithe/Mosques/Feed the World/Reliquary religion (almost ideal for this build, just need Pagodas instead of Mosques). Thebes was my lowest hammer city (!) for a lot of the game, and most of the key wonder building happened in Elephantine, Memphis, and Alexandria.
I finished both technology and culture at t195, so sub-200 was absolutely doable here. Unfortunately, I had gold trouble and had to wait it out. Askia was sitting there with 10,000+ gold but wouldn't be my friend. Painfully close to a glorious sub-200 with a bizarro strategy, but I'm satisfied that the approach is sound in practice.