Yeah, I didn't build as many Wonders as I would prefer to. Entirely my fault though; as noted, I made a lot of mistakes.
The trick to really hitting the ground running in these settings is to do a two-city NC start. You were close when you theorized the single city, NC beeline. However, it just doesn't generate enough

to expand, get the GL and make enough units to deter early wars.
The seriously counterintuitive bit is that executing this requires building a Library in both cities,
then building the Great Library in the second city to grab Education while you build the NC in the capital to push through Classical and Medieval.
Perfect dirt involves 3

tiles so that you can avoid having to slap up a Granary in the second city, as well as enough Forests to chop the Library in the second city and the NC in the capital. (You can buy the Library in the second city if you must, though this will cost you an RA later.) Being able to go Scout -> Worker rather than Scout -> Scout -> Granary in the capital is also helpful. You want to hit an early

ruin to get a head start on growth and

in the second city, as well as either Mining or something on the Philosophy beeline, for the absolute fastest time.
Once you get the NC, you want to spam at least two Settlers from the capital to improve

production. I also will sometimes build a Settler rather than a Monument to delay the GL in the second city, depending on circumstances. Otherwise, getting Rationalism (via bulbing Astronomy from the PT) before RAs start resolving is difficult. Depending on whether or not you hit a ruin, you should have Education by turn 60-65 from a strong start. Research CS and Theology down to a single turn to extend the amount of time AIs have to hit Classical for as long as possible, and sign RAs each turn as you near Medieval. Build and staff Universities in the first two cities after Education lands, then start Hagia/Oracle.
You should be trading and looting the AIs for cash every time you can, prioritizing cleaning out the AIs that have high GPT. What you don't want is two AIs that have 200

at the same time.
As noted, hard tech Compass (and Metal Casting if you hit a tech ruin at the beginning), leaving MC/Steel as the median, Navigation as the expensive tech and a backward tech like The Wheel as the only other option. Get to Steel and then push through the center to Chivalry, then through the bottom to Gunpowder, then back into the center as far as you can on the first wave of RAs.
After that the game more or less plays itself. You want to get Hagia -> ND, pick up the Oracle, and get the Louvre and Brandenburg if at all possible for GAs. You need Freedom and Scientific Revolution on the SP front. Everything else is negotiable. Maximize the number of Great Scientists you get (rushing a Public School in the bottleneck), get to Rocketry as soon as you can without compromising your ability to complete the tree with GS/Scientific Revolution/Oxford, slap up Apollo while building Factories and Spaceship Factories in other cities, buy the capital's Spaceship Factory and win.
If everything comes together, I believe that you can win in the 170s. The 180s are a much more realistic win.