I've played three games now, and one thing I noticed is that the end of the game comes very fast. It seems once you have three cities up with buildings, everyone is getting a tech almost every turn (especially with the 9+6 trade for a silk ability), and everyone who was originally focusing on military is now in a race to get a tech victory (or abandons their plan to beat the other players to it). On top of that, one player who has culture everywhere can move 2 or sometimes 3 spaces on the culture track each turn, even at level 3, which basically sets a timer on the end of the game since it's pretty tough to stop a player from doing that.
We've discussed it among ourselves and recognize this to be a problem; it's one thing that makes it very different from the computer game. If we had some more time to move around and actually fight each other with similar-level units, it would make for a more tactically strategic game and not just rushing for victory by combining a few abilities in the right order.
I would speculate the problem comes from the game designers being pressured to make a game that ends quickly. At some point, the game will snowball and someone will win, just to cut two hours off the game time. It feels a bit too chaotic when you've invested 2 hours already into setting up your cities and building an empire. In the computer game, someone might go to war 3 or 4 times in a game, and the pace of the game moves fairly linearly as you progress through time. In this game, you're lucky to have 2 or 3 battles before it's over, and it's not uncommon airplanes to fly over barbarian villages. There's just no opportunity for dynamics to evolve between players - it just ends.
One thing that I think would definitely improve this is by slowing the rate at which technologies are learned. Less frequent new technologies means less crazy special abilities, more production to spend on military units, and more battles between similarly matched forces. To do this, I would increase the trade limit, and proportionally increase the trade cost of technologies. It makes sense to have to save up for a few turns in order to get a level 4 tech, not get one every turn.
This would slow down the military victory, as it would take longer to build up a force strong enough to wipe out a capital, and also give players more time to trek over to your land and attack your units.
Slowing technology would slow down the economic victory automatically, because most of the ways to get coins requires having those tech cards. We haven't had a player go for economic victory yet, so I'm not sure how that might need to be balanced, though.
Cultural victory can happen pretty much independently from technology, so it would have to be limited on its own. The winner of our last game moved through level 3 culture in 2 turns, by getting well over 20 culture per turn (using scouts, resource abilities, etc.). We think a simple way would be to change the culture income to work the way hammers do. When you devote your city to the arts, you can move one (and only one) space on the track, per city that you do that action with. You have to be able to afford the movement with the culture icons available to that city (plus scouts can gather for it, or you can add incense abilities the same way wheat does for hammers), and additional tokens are lost. That means you can't just bank up culture tokens and spend them later.
Rebalancing these rules would probably be a matter of adjusting the trade limit and tech costs. Level 1 techs should still cost 6 or maybe 8, but level 3 or 4 techs would be more along the lines of 30 or 50. Next time if we try these rules, we will watch how long it takes the cultural player to move up the track, and then we can readjust the tech costs so that everyone else's technologies are earned at roughly the same pace.
Sure, a few little rules might also have be visited, like when you loot a player there won't be any culture tokens to take, but maybe you can get trade instead and then allow using trade to get culture (like hammers) at 3:1. But after working out those kinks, it shouldn't be too difficult to just slow down the pace of the game at the end, since in its current state it feels like we're not seeing the potential we could be from what is a fundamentally very good strategy game.