A variation of this could be that instead of the parasites going full zombie, they would quietly infiltrate top level individuals in the patient zero empire that would start a faction that would inexplicably take over the empire and then spread to any empire on good terms / open borders with that empire. Once the rest of the galaxy figures out what's happening they have a growing federation working to advance the cause of the parasites, that's still trying to recruit more members. If the player gets hit with the parasite faction they can choose between resisting (causing internal disharmony, but also reducing the effectiveness of the parasite faction since they're more in the open now) or embrace it and fight against the rest of the galaxy on behalf of their brain slug overlords.
I think a crisis should not automatically kill the empire in spawns in.
BTW one thing that can be leveraged when you make a crisis "ancient" (any kind of crisis) is that you can start an event chain where you need to send your science officers (with escort maybe) around the galaxy to uncover hints on how the empires of the past dealt with the crisis. It could be interesting imho. (maybe a virulent crisis could make empires less keen on opening borders with infected empires)