Nothing like writing a battle report so late that you forget most of the details. Here is what I remember the mission was pitched battle, kill points with the corsairs getting turn 1. The sisters won by 1 kill point 7 to 6 or maybe 8 to 7. I used a similar list to the one I used here minus the warp hunter. This list will always have problems in kill points but if I could suppress the exorcists early I figured I'd be in good shape. This worked to a point, I was able to stun lock them for a couple turns but one turn four (I think) I was unable to stun them and they went 3 for 2, destroying my falcon (breaking the unit inside who never regrouped) and my bomber.
What the game did teach me is that I need to consider making a second prince a mandatory part of my list. They are probably overkill vs. hth armies, but vs. shooting armies they are needed because even if the corsairs get an alpha strike in they are so fragile that the return fire from a shooting army will cripple them. I would probably drop the war spiders in exchange for a prince and a unit of fire dragons.