I think (though I can't confirm it yet) that there's a bug with the autosave. Think about it - autosave happens when you hit end turn, not when your turn starts, right? And the problems start when turn processing begins, starting with the save if it's needed.
I disabled autosave, mashed the turn button and didn't get a hang. It's not much of a test. Still have to see how things work when the game's been running a few hours and I've actually been playing instead of mashing 'Turn.'
I remember that there was a similar autosave problem with GalCiv II if there wasn't enough memory available, so it's worth looking at even if it's just to eliminate that possibility.