Since the patch, no matter what save I load, no matter how many new games I start, within 3 turns either I or the enemy will hang mid-turn. It could be be moving a unit that never moves but never gives me back control or an enemy turn that never ends, either way I can no longer play the game.

Had the same Problem here, after using Jump Jets the Turn freeze and I cant go any further.
After uninstalling the game and clean re-install all works fine so far.

Thanks for pointing that out. Re-installing...