I must have been pretty unlucky to get the Scourge at 2350 compared to what many of you have said, though the event can trigger at 2320.
It does seem that the only contributing factor to your ability to deal with these events and the Fallen Empires after 2300 is probably your size. By then, assuming you've kept research at pace with your population growth, you should have Tier V in at least one set of weapons, plus Tier V shields, armor, etc. The AI certainly does a good job of keeping pace on the tech, they are always around the Tier IV/V mark at 2300.
I'm also surprised that some of you have managed to avoid the crisis for so long, the Scourge are the default one, so if you don't have the tech to trigger the other two, as each 20 or so years pass from 2320, the chance to see the Scourge increases as well. To have gone another 100 or more years before a crisis triggers is extremely lucky (or unlucky depending on your view).
Still, trying my hardest to get the Unbidden this time, but the tech just doesn't appear often enough.