Two solo tests and another live 4p test have led to some further progress. The change, suggested by a playtester, to replace the common decks of Chronicle cards with an individual deck for each player has proven successful; not only does it have the intended effect of making it harder/less valuable to bring another player below the threshold of his scoring card (because cards are now placed face-down), but it also puts all of the scoring information right in the players' hands, making it easier to play.
Our live session lasted 3 epochs and while it was still anyone's game, we chose to quit due to the hour. The scores were fairly high for the end of the 3rd epoch, with the leader having 40 points and other players in the high 20s and low 30s. This was due, we believe, to two players having Democracy (helps you keep Unrest down inexpensively) and the other two had Emulation (lets you use an ability that another player holds), so everyone was able to keep their Unrest low.
We found that a 3 epoch game is not unsatifsying. I could see making a quicker-playing variant in which you choose any one of your initial 3 advances and implement it for free, and then just play as usual for 3 epochs instead of 4.
One of the players brough up the question of balance, specifically with respect to luck of the draw with the 4 structures tiles and 3 advance cards that form your hand. He suggested that having a hand of structures wasn't exactly interesting or important and these could just as well be drawn freely from the supply when you build. I tested this through and it does indeed seem fine. He also noted that there can be great disparity in the initial deal of advances. As I thought about it more, I realized that there are essentially 3 types of advances in the game: ones that are always useful and powerful no matter your strategy; ones that are more focused but are useful enough that you can build a strategy around them; and ones that are useful if you happen to be in a certain situation. To smooth out the luck of the draw, at least to start, I proposed dealing each player one "always useful" advance and two "strategy-specific" advances. This ensures that everyone gets one and only one powerful advance, and no "situational" advances, which don't really matter till later in the game.
It's encouraging that after each of the last two sessions, the changes have really been related to refining the way existing systems work, rather than re-envisioning entire systems or making big, sweeping changes. I think all that remains is to balance the advances a little bit to soften a couple and strengthen a couple others, and then it should be very close to done.