I'm open to changing games and the reasons for doing so certainly make sense to me, but there is a certain appeal to Imperialism.
I think PBEMs have a certain momentum to them. If the pace is quick, then everyone feels some motivation to keep up the pace. If the pace is slow, it is easier for everyone to take the extra day or two to play their turn. At least, I feel this way.
How about this: We use the in game hot seat timer and set a time limit of how long a turn can take. From the time you open the last player's saved game until you make your own saved game can be at most, say, 30 minutes. After that, you can look at the game as much as you want to make plans for your next turn or conduct diplomacy, but the time it takes to pass the game on to the next player is limited.
This means that small nations can do more micromanaging and so have an advantage. On the other hand, this might simply counteract the advantage that the big nations have and actually make the game more balanced. I would be happy to trade civs if anyone thinks that small civs are too favoured in this approach.
Personally, I think introducing the real time element detracts from civ somewhat, but, on the other hand, this game will take years to complete without it. I would rather play an "imperfect" game of Imperialism that actually goes somewhere than a "best practices" game of Imperialism that never makes it to 1872.