It might have been suggested before, but anyway:
1) I'm currently the victim of a massive slowdown where distant NPR wars I'm not involved in cause the game to compute the next month almost in real time. I don't mind waiting a little, there's always something else to do while Aurora is busy, it's just that a 30-day auto turn could take a minute to compute, or two hours. When I'm expecting it to take a long time, I read or cook dinner or make myself useful in other ways than commanding my star empire. I stop checking once a minute if the turn is finished. But then, maybe the next time I hit "30 days" the distant battle or war is over, the turn is done in 20 seconds and the game waits for my next input while I read the sports pages, just to pass the time. That effectively doubles the time it takes to get through a slowdown phase.
What about an option "Play a sound if the last turn took longer than 3 minutes to compute"? Just a notification that you're expected in the command center again.
Also, the event log might include a message saying that "A distant battle has caused some game slowdown". So new players know it's not a bug.
2) If the slowdown is due to such a war, what about an SM option to "End distant NPR wars"? It would simply restore all NPR relations to a state of harmonious co-existence and make the game playable again. Of course that would be a massive intervention in the history of the galaxy, but so is removing entire star systems.