First of all, VERY interesting game to read. I rarely play the higher difficulties because I just don't enjoy the necessary playstyle, but it's always impressive to see a group succeed so well with such a bad starting situation at those levels. Unfortunately, I think one of the things this succession game shows is how little difference your choice in civs makes; taking the arguably worst civ in the game simply meant that you played a game using a generic strategy instead of building around those little boosts particular to your civ, but the generic strategies are strong enough to stand on their own merits.
On to the discussions:
There's a lot of balance tweaks that could be done but I'm not sure if any of them would really change the basic economy system of this game.
I think there are a lot of things that could be done to change the basic economy.
For instance, let's take city size. Currently, the base research rate depends only on TOTAL population, and trade route income depends only on the total population of your non-capital cities. So ten size 5 cities are just as good as five size 10 cities, but thanks to the semi-exponential growth curve, the multiple small cities are easier to get. (Add Maritimes and it gets worse). And those ten small cities will cover more land area, meaning higher chance of having more types of luxuries and higher chance of having the strategics you need within your border. Expanding, as a result, pays for itself, which makes it incomprehensible that the AI (especially on lower difficulties) seems to set expansion at such a low priority. I had a game recently (on Prince, admittedly) where England never even settled a second city; my sixth and seventh cities ended up boxing them in, but it should never have come to that.
But what if these relations weren't linear, any more than the growth equation is? What if the first five population of a city gave 0.5 gold per pop in trade income and 0.5 research per pop? And the next five gave 1.0 in each, and the five after that gave 1.5 in each? Or let's say it's more gradual, with 0.5 for the first citizen, 0.6 for the second, 0.7 for the third, and so on up the line?
Would ICS still be the way to go? Or would you finally have a setup where few, large cities is a better design than many, small cities?
And there are so many other little possibe design tweaks, many of which have showed up in other mods already. What if the game had Tech Diffusion like previous games, where a civ that falls behind gets bonus beakers when they research something their opponents already know, so that you won't see Greece throwing hoplites at your Mech Infantry? What if there was a larger penalty for keeping a puppet? What if more mid-tier techs required more techs from the other branches of the tech tree, so that it was impossible to slingshot three techs up a single line at once?
Yes, these are all things the developers should have looked into before releasing the game. I'm not excusing their laziness. But the point is, if it's so easy for us to come up with possible solutions to the most egregious problems, is it really hard to imagine that six months from now this game could be as fun as we hope it would be? (This is why I spend most of my time in the modding forums. People don't spend as much time complaining about the game-as-is, and more time thinking of ways to fix and/or expand it.)