Well, since you asked…
That music gambit, as you called it. Was exactly that, a Gambit for trying to get it so late. As expected, you failed to get the GA. Well, no game breaker there, but at that point you should have bowed out, since you had no intention of building Sistine and there was no longer the big GA payoff.
What you should have done at that point, was teched after theatres. This one isn’t beelined by the AI’s so you would still be able to trade it around for plenty of stuff. But also importantly, it would then give you an additional 20% discount to then finish off teching Music.
Earlier you were debating on going after TGL at around 750 BC I believe. This one is hardly considered a gambit. IIRC you had no marble, and were not industrious. You also had no real production piles around and since often TGL is gone 1000 BC… I think you were grasping at straws there
I try to aim for it being completed before 500 BC, and this will still cause a lot of failures.
Anyhow, I think this is one of those rare games where building the Globe in the capital was a decent move. I would have farmed the plains and ran one huge MOFO SE farm in there. I would have blasted my way up to rifling with that. At the same time, I would have had a monster whip-factory, and this means everything, infrastructure, and units.
When you get to rifles, you would be able to draft a UU every round, AND you would be able to whip at the same time. You could get 2 units out of that city in a single turn for many turns. Then, you stomp over whoever you want with that.
BTW, in that last save your capital looks weird. You are still bleeding off a whopping 5 food a turn, but still working two farm tiles. This doesn’t make much logic to me. The last thing you should be doing when bleeding off food is trying to grow another pop. Yet I see the capital is trying to convert hammers to beakers, and yet you are not even working that monster copper-hill tile. I fail to see the point of spending another 6 turns just to grow another pop level, when this will cause you to yet bleed off even MORE food. That’s a lot of waste going on there.
It’s particularly weird to see you are also working a simple plains-hill at the same time. Maybe that war was a bit too distracting?
Anyway, there is more ways to skin a deity cat, I’ll stop here before you get mad at me
Nested stuff like x^x and the division will wreck you.
I'll try to draft 3 redcoats each round if possible (since that's the max. standard size gives me).
This easily sets my record for the largest early city size I've ever had. I saw USun get a size 19 capital at 300 AD so that size is my next goal. 
