I went through this as well, but for me, the event did not end after x amount of time. Instead, after I sat at the computer to check cameras to see if some radar pings were boars or eggs at some sats I needed to go visit, I got the game-triggered crash: lines slowly crossing the screen, a surge of despair, and me saying "Noooo, not like this!" I am not sure if something else happened at the same time—perhaps my floating black rectangle came to give me a hug cause it knew the egg-demons were scaring me—or this is potentially a randomized outcome from the event itself.
I loaded the last save and no egg ships ever visited.