Strategy for succeeding at Crisis skill checks
Crisis Deck Management

You haven't put much emphasis on crisis deck management, which is important.


You can scout to bottom deck crisis cards.
Roslin can select one crisis out of two on her turn.
Boomer gets to see the next crisis before it is revealed.


All of these abilities can mitigate the damage caused by failing a crisis.

Track Destiny

You can keep track of destiny, so you can avoid playing when its stacked against you.

Evil and clever brig hack

If you can get around the players personal objections to this, having a player (even human) in the bring increases the number of skill cards drawn per crisis.  

Imagine everyone is in the brig.  Then you can cycle through the skill deck, getting all of the best cards into players hand before ever having a crisis check.