I'm not sure how engaging a hyperkane shuffle would be - especially at a point in the game where players can build Gateways with jump-capable construction ships - but non-combat Crisis that has to be solved with technology, diplomacy, and the like would be great.
The disease example is a good category.
1) Timer - pops slowly die as the plague degrades internal organs and circuitry. Every planet gets a Purge modifier. This modifier generates events, as the empire has to deal with leaders dying off and society breaking down.
2) A cure must be researched, with a high cost in engineering/society, depending on empire. Empires who sign Research Pacts gain a bonus.
3) Various pop up that grant bonuses to researching the plague that science ships investigate.
Or - Doomsday Device
1) An artifact of doom left by an ancient civilization has broadcast a message that it will destroy the galaxy. Destructive pulses cause Devistation to slowly increase on all planets, killing pops. Events must be managed.
2) Ruins must be scoured for the location and nature of the artifact. Precursors can be convinced to help, or conquered. The Curators can give clues.
3) Empires can share findings - or horde them for themselves.
4) Empires that uncover the nature of the artifact can deactivate it - or just protect themselves from its effects, for a huge diplomacy malus.
The disease example is a good category.
1) Timer - pops slowly die as the plague degrades internal organs and circuitry. Every planet gets a Purge modifier. This modifier generates events, as the empire has to deal with leaders dying off and society breaking down.
2) A cure must be researched, with a high cost in engineering/society, depending on empire. Empires who sign Research Pacts gain a bonus.
3) Various pop up that grant bonuses to researching the plague that science ships investigate.
Or - Doomsday Device
1) An artifact of doom left by an ancient civilization has broadcast a message that it will destroy the galaxy. Destructive pulses cause Devistation to slowly increase on all planets, killing pops. Events must be managed.
2) Ruins must be scoured for the location and nature of the artifact. Precursors can be convinced to help, or conquered. The Curators can give clues.
3) Empires can share findings - or horde them for themselves.
4) Empires that uncover the nature of the artifact can deactivate it - or just protect themselves from its effects, for a huge diplomacy malus.