After quite a bit of prodding, I finally managed to convince a friend to buy this game so that we could play multiplayer games.
When we tried to play, the game consistently became stuck between turns, with "WAIT" appearing indefinitely in the bottom-right of the screen where the turn button should have been. We tried to load our autosave three times, with the same result each time after a few turns.
It looks like this issue was submitted to Stardock on April 8, 2014, at which point it was to be "submitted internally to the team":
https://forums.galciv3.com/453398/page/1/