First off: Going for astro was a complete failure: Mansa already had it, the others didn't have anything interesting to trade and I was completely stuck. Well, I "reloaded", meaning I continued from my 780AD save with one turn to Lib. I went for Lib took Nationalism and everything went much better...
However, I skipped the Tay, because (1) I didn't have marble, (2) Sparta didn't produce as much as it does now and I wanted it to get the GT asap and (3) I only produced GS's - Mansa took it a few turns later, so I wouldn't have had a chance anyway.
Techs: Lib -> Nat (for free) -> Drama -> Printing Press (partly bulbed) -> ... -> Gunpowder -> Rifling
Traded again quite a bit. I don't remember everything exactly anymore. I traded Edu to Sal und JC. Sal, I think, gave me Guilds and JC, one turn later, Banking. Or maybe it was the other way round. JC also paid me quite some money which I gave him back (together with Music) one turn later, when I bought Engineering from him. I think I got Music from Sal, but I don't remember if that was the Edu-trade or another one).
I also sold some of my resources to the others civs (Sal and Mansa in particular). The best trade being silk (or so) for 15 gold to Mansa.
I got another GS in time to partly bulb PP. Afterwards I only needed 4-5 turns to research it. That was perfectly timed

(but the timing wasn't planned, only luck

), because one turn before I got it, Mansa appeared. I waited a turn (to get PP) and then I saw that he already had Replaceable Parts, but neither Nat nor Lib. He wanted both for RP.

But I needed RP really badly (to outpace Sal and the others on my continent), so I gave in. However, Mansa was fair: 2-3 turns later he offered me Econ for free!!!

I never received such a generous gift before!
My next GS I used for a GA to speed up Rifling which I will hopefully get exactly at the end of the GA.
Right after I got Drama, I built theaters everywhere to start the GT, which will be finished in a turn in Sparta. Now, I try to produce some CR Maceman. I was too afraid of adopting any religion, so there was no sense in switching to Theocracy (thus I never even researched Mono and Theol).
Civics: After getting Lib I switched to Free Rel and Caste System, at the first turn of my GA I switched to merc (like all the other civs on my continent) and back to slavery as I will whip a bit more: If I start a war with Sal, I will lose two happy resources, so I have to prepare for that (and I would like to draft a bit...)
The
Map:
The tech situation right now is quite comfortable: Sal and JC have neither RP nor Nat, Isa has Nat, but is otherwise way behind. I think, I will go for Sal first, since he is the fastest techer on my continent, afterwards I can turn to Isa.
Other civs: Btw, Isa and Sal are still fighting each other, how nice.