Very solid play, OtsoMaki!
The only minor quibble I have is worker micro around Timbuktu - we could easily have it so that the NE would be finished this turn and we'd get the Philo-bulbing scientist with double speed. Then our empire would be ready to start the GA. Maybe I didn't stress the importance of this enough.
Hatty going Theology was a bit unfortunate, let's hope her next tech choice won't be Divine Right.
I checked the save and estimated that we're 154 turns from optics with 10% research which is our break even point with +3 gpt. Now of course we'll be faster than that with things like failgold and binary research and so on but still it's a long road.
You are right that our

per turn is very low, but that shouldn't come as a surprise. Did you forget my proposition that our research towards optics-astronomy will come from scientist bulbs? My original thinking was that we'd not only have optics but also astronomy by 700 AD. We were sloppy with getting GLib-NE up in optimal time, so those turns are a direct delay to our astro date. Also Hatty is not being helpful with the trades. Anyway, I'm in utter shock if we don't have astro by 1000 AD (T160, 41 turns from now).
I think this makes failgold very important since cottaging anymore isn't so strong option and we have good resources for it and we have hammers (we're first in the world in prod). SP can go theoretically anytime now. We are able to delay HE as long as we want for failgold though, but we can't use our best prod city Uruk for that. 3 monuments could open Zeus statue for us too.
Agree that the time of cottaging is pretty much over. Good thinking on the HE-failgold! Not a fan of putting 90

to monuments to be able to failgold SoZ.
My techpath from here would be compass-metal casting(if it can't be traded)-machinery-optics. I think we can count on Hatty teching at least calendar (typical ai tech) for us in that time(though if she decides to go fo MoM, she might not trade it for us right away).
I'll think about the next tech a bit and return to it in my PPP. Are you sure that a friendly AI will deny you a trade for "we have our reasons."(=the AI is building a wonder attached to the tech)?
@OtsoMaki: Are we getting any GLib-failgold next turn?
edit: my understanding on how fog-busting works: the unit prevents barbs from spawning 2 tiles to each direction, like this:
Thus, the warrior should be 1NW (or 1NW 1W to prevent barb galleys from appearing). Correct me if I'm wrong.