It's hard to tell with just one save so late in the game, but it looks like your are on the right track. What happens when you move up to Immortal? I would suggest moving up in difficulty, you are crushing everyone in science.
A couple of things:
- Your population is a bit low in your capital. I would advise using early trade routes to bring food to your capital, especially as you went tradition. This will get you more base science. Early and mid-game should be all about growing as fast as you can.
Yes definitely, I usually have 30 pop capitals but this game has not been a good food game
- You still have quite a bit of the tech tree left, how many great scientists did you pop and when? Right now I see three settled academies, that is about right. I actually suggest just one or two. The rest of the scientists should have helped you get through the late game science.
I go by the theory that once you reach Atomic Era you should just rush them after eight turns of max science, is that wrong
- The Musician's Guild should have been built long ago for culture. Also, if you have the opera house's up, you should have finished Hermitage as soon as possible for more culture.
I didn't want too many specialist and I was having trouble deciding what city to build it in along with a good-time build it (Trust me, in all other games I go for that right once I get access to it as I play a pretty heavy culture/tourism game usually
- You have no faith generation, which can be used to buy more great scientists or great engineers. I would suggest getting a few faith buildings. As you have a lot of the patronage tree done, you could ally some religious city states and at least shoot for 1 faith bought great person.
I never built faith buildings as I knew I would've been over-ran by the Celt's religion which I already was, but you're right, should've done it just for the great people
- You don't seem to be building Hubble, which should be a priority. It gives two free great scientists and a spaceship factory to finish parts in the capital. Right now you are building them in your satellite cities and they will probably finish before you are done with the science. Ideally though, you'd be able to get through the late game science faster with great people and use freedom to purchase the last couple of spaceship parts.
I was getting a Great Engi in 10 turns so my theory was just building research now and let me rush it once the Engi spawns in the capital. Not that anyone else was close to reaching it so I could be lenient with it.
- You only have 5 workers and from what I can tell you had a 5 city empire before going after Rome. You would probably want at least 7, I still see some unworked tiles in your empire and some with fresh water access. You could have farmed those for more growth.
I think that I was expecting more GPI's so that's why I didn't improve.
Overall, I don't see any glaring mistakes. I think you are pretty much ready to move up in difficulty.