If this is of any value or any kind of help, I made a silly video of our last Twins (blue first) kill. You can see that we DID get stuns in the raid, yet, it wasn't fatal. As I said before, have hots rolling on tanks and you mostly will be fine, as well as having a healer outside of the 2 camps for healing the warlock and cleansing his debuffs with shadow blades/Shadow nova.
The video has acceptable quality and it's very compressed ( 31MB ).
Conspiracy VS Eredar Twins - FileFront.com
As said before, it's kind of funny that using a Blue first start is easier, yet, it gives more loot. You can even bring an extra healer to a blue first strategy and not worry about enrage timer and phase 2 with red start is more healing intense than blue start.
@Regen: Wiping on a downed boss due to bad luck is less annoying that wiping on that same pull cause of a mispull.. or 4 misspulls. I'd say luck is a part of this fight, just like Vael when people were still in some MC gear and he'd BA healers all the time.